A390836 - OEIS

%I #14 Mar 03 2026 14:37:28

%S 2,3,24,362880,20922789888000,15511210043330985984000000,

%T 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000

%N 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).

%C The next term is too large to be displayed.

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

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

%C See also comment in A390815.

%e For n = 4, 4!/sigma(4) = 24/7 and 7 does not divide 24, so 24 is a term.

%e For n = 5, 5!/sigma(5) = 120/6 and 6 divides 120, so 120 is not a term.

%o (PARI) isok(n) = ((n! % sigma(n)) != 0); \\ A325436.

%o for(n=1,1000,if(isok(n),print1(numerator(n!/sigma(n))", ")))

%Y Cf. A000142, A000203.

%Y Cf. A325436, A390815.

%K nonn,frac

%O 1,1

%A _Claude H. R. Dequatre_, Feb 17 2026