A343424 Numbers k such that sopfr((k-1)!) is divisible by k, where sopfr(k) = A001414(k) = sum of primes, with repetition, dividing k.

1, 2, 45, 53, 177, 436, 1239, 3651, 6463, 6869, 10753, 19450, 29721, 33289, 88907, 93682, 1137232, 1516121, 4361271, 9428534, 43778664, 74738670, 271442366, 775223371, 835126289, 1736463189, 3088442241, 5054888590, 11184483614, 16993011938, 30788570768, 33342871740

Offset: 1

Author

Scott R. Shannon, Apr 15 2021

Keywords

• nonn

Comments

See A025281(k-1) for the values of sopfr((k-1)!).

Examples

			45 is a term as sopfr(44!) = 585 which is divisible by 45.
		

Links

• Martin Ehrenstein, Table of n, a(n) for n = 1..35

Crossrefs

Cf. A001414, A025281, A027746.

Programs

Mathematica

sopfr[0] = sopfr[1] = 0; sopfr[n_] := Plus @@ Times @@@ FactorInteger[n]; sum = 0; s = {}; Do[sum += sopfr[n]; If[Divisible[sum, n + 1], AppendTo[s, n + 1]], {n, 0, 10^6}]; s (* Amiram Eldar, May 06 2021 *)

PARI

sopfr(n) = (n=factor(n))[, 1]~*n[, 2]; \\ A001414
isok(k) = !(sopfr((k-1)!) % k); \\ Michel Marcus, May 06 2021

Extensions

a(27) from Amiram Eldar, May 06 2021

a(28) and beyond from Martin Ehrenstein, May 16 2021