A390836 Numerators of ratio n!/sigma(n), when the denominators are > 1 and where n! = factorial(n) (A000142) and sigma(n) = sum of divisors of n (A000203).

2, 3, 24, 362880, 20922789888000, 15511210043330985984000000, 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000

Offset

1,1

Comments

The next term is too large to be displayed.

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

All terms are even, the third is 24 and all the next ones are multiples of 24. (verified for n <= 10^5).

See also comment in A390815.

Links

Table of n, a(n) for n=1..7.

Example

For n = 4, 4!/sigma(4) = 24/7 and 7 does not divide 24, so 24 is a term.
For n = 5, 5!/sigma(5) = 120/6 and 6 divides 120, so 120 is not a term.

Prog

(PARI) isok(n) = ((n! % sigma(n)) != 0); \\ A325436.
for(n=1, 1000, if(isok(n), print1(numerator(n!/sigma(n))", ")))

Crossrefs

Cf. A000142, A000203.

Cf. A325436, A390815.

Sequence in context: A326226 A291262 A307922 * A383578 A048674 A320223

Adjacent sequences: A390833 A390834 A390835 * A390837 A390838 A390839

Keyword

nonn,frac

Author

Claude H. R. Dequatre, Feb 17 2026

Status

approved