A379928 Numbers m such that A379742(m) is a multiple of A027423(m).

0, 1, 2, 10, 17, 26, 30, 36, 43, 57, 58, 67, 73, 74, 82, 99, 103, 105, 114, 125, 129, 138, 147, 161, 165, 173, 186, 194, 201, 237, 239, 261, 269, 275, 291, 299, 314, 315, 317, 345, 347, 375, 377, 381, 383, 387, 402, 411, 413, 437, 447, 458, 467, 485, 495, 506, 513, 515, 519

Offset: 1

Author

Michel Marcus, Jan 06 2025

Keywords

• nonn

Comments

Apparently, almost all the terms are odd (asymptotically). Among the first 10^4 terms there are only 43 even terms, and only 2 of them, 0 and 36, are divisible by 4. - Amiram Eldar, Jan 15 2025

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 2..114 from Michel Marcus)

Crossrefs

Cf. A000142, A000178, A027423, A379742.

Programs

Mathematica

Select[Range[0, 520], Divisible @@ DivisorSigma[0, {BarnesG[# + 2], #!}] &] (* Amiram Eldar, Jan 06 2025 *)

PARI

isok(m) = numdiv(prod(k=1, m, k!)) % numdiv(m!) == 0;

PARI

isok(m) = {my(prd = 1); forprime(p = 2, m, prd *= ((1 + (m*(m+1)/2 - 1 - sum(i = 2, m, sumdigits(i, p)))/(p-1)) / (1 + (m - sumdigits(m, p))/(p-1)))); denominator(prd) == 1;} \\ Amiram Eldar, Jan 15 2025

Extensions

a(1) = 0 inserted by Amiram Eldar, Jan 15 2025