58 (number)
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Cardinal | fifty-eight | |||
Ordinal | 58th (fifty-eighth) | |||
Factorization | 2 × 29 | |||
Divisors | 1, 2, 29, 58 | |||
Greek numeral | ΝΗ´ | |||
Roman numeral | LVIII | |||
Binary | 1110102 | |||
Ternary | 20113 | |||
Senary | 1346 | |||
Octal | 728 | |||
Duodecimal | 4A12 | |||
Hexadecimal | 3A16 |
58 (fifty-eight) is the natural number following 57 and preceding 59.
Mathematics
Fifty-eight is the seventeenth discrete semiprime[1] and the ninth with 2 as the lowest non-unitary divisor; thus of the form , where is a higher
58 is equal to the sum of the first seven consecutive prime numbers:[2]
This is a difference of 1 from the seventeenth prime number and seventh super-prime, 59.[3][4] Furthermore, is semiprime (the second such number for after 2).[5]
Fifty-eight is an 11-gonal number, after 30 (and 11),[6] and it is a Smith number.[7] Also:
- 58 is the second member of the fifth cluster of two 1, 0) in the 13-aliquot tree.[10]returns .[12]
- 58 is the smallest integer in decimal whose square root has a continued fraction with period 7.[11]
- Given 58, the Mertens function
There is no solution to the equation , making fifty-eight a noncototient.[13] However, the totient summatory function over the first thirteen integers is 58.[14]
The regular icosahedron produces fifty-eight distinct stellations, the most of any other Platonic solid, which collectively produce sixty-two stellations.[15][16]
Coxeter groups
With regard to Coxeter groups and uniform polytopes in higher dimensional spaces, there are:
- 58 distinct uniform polytopes in the fifth dimension that are generated from symmetries of three Coxeter groups, they are the A5 simplex group, B5 cubic group, and the D5 demihypercubic group;
- 58 fundamental Coxeter groups that generate uniform polytopes in the seventh dimension, with only four of these generating uniform non-prismatic figures.
There exist 58 total
In mythology
Belief in the existence of 58 original sins by several civilizations native to
Other fields
58 is the number of usable cells on a
References
- ^ Sloane, N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007504 (Sum of the first n primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-20.
- ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-20.
- ^ Sloane, N. J. A. (ed.). "Sequence A006450 (Prime-indexed primes: primes with prime subscripts.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-20.
- ^ Sloane, N. J. A. (ed.). "Sequence A104494 (Positive integers n such that n^17 + 1 is semiprime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-27.
- ^ "Sloane's A051682 : 11-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- ^ "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- ^ Sloane, N. J. A. (ed.). "Sequence A001358 (Semiprimes (or biprimes): products of two primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-27.
- ^ Sloane, N. J. A. (ed.). "Sequence A001065 (Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-27.
- ^ Sloane, N. J. A., ed. (1975). "Aliquot sequences". Mathematics of Computation. 29 (129). OEIS Foundation: 101–107. Retrieved 2024-02-27.
- ^ "Sloane's A013646: Least m such that continued fraction for sqrt(m) has period n". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-03-18.
- ^ "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- ^ "Sloane's A005278 : Noncototients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- ^ Sloane, N. J. A. (ed.). "Sequence A002088 (Sum of totient function.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-27.
- ISBN 978-1-4613-8216-4.
- ^ Webb, Robert. "Enumeration of Stellations". Stella. Archived from the original on 2022-11-26. Retrieved 2023-01-18.