A390815 - OEIS

A390815

Denominators > 1 of ratio n!/sigma(n), where n! = factorial of n (A000142) and sigma(n) = sum of divisors of n (A000203).

3, 2, 7, 13, 31, 31, 127, 307, 1093, 1723, 2801, 3541, 8191, 5113, 8011, 10303, 19531, 17293, 28057, 30941, 30103, 131071, 88741, 86143, 147073, 524287, 292561, 459007, 492103, 797161, 552793, 579883, 598303, 684757, 704761, 732541, 735307, 830833, 1191373

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OFFSET

1,1

COMMENTS

First fractions n!/sigma(n) in their reduced form are: 2/3, 3/2, 24/7, 362880/13, 20922789888000/31, 15511210043330985984000000/31...

Conjecture: all terms are prime (verified for n <= 10^5).

Conjecture: for n >= 4 if sigma(n) does not divide n!, then n is a square. (verified for n <= 10^5).

See also comment in A390836 (numerators).

Is this the same as A062700 from the 3rd term on? - R. J. Mathar, Mar 06 2026

LINKS

Table of n, a(n) for n=1..39.

EXAMPLE