A341129 Numbers k such that A341117(k) is divisible by k and k is not a prime or power of a prime.

42, 54, 66, 78, 102, 114, 135, 138, 147, 156, 162, 174, 186, 192, 222, 228, 246, 250, 258, 282, 318, 354, 366, 372, 402, 426, 438, 444, 474, 498, 507, 516, 534, 582, 606, 618, 642, 654, 678, 686, 732, 762, 786, 804, 822, 834, 845, 876, 894, 906, 942, 948, 978, 1002, 1029, 1038, 1074, 1083, 1086

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 05 2021

Keywords

• nonn

Comments

If k is a prime or power of a prime, A341117(k) is divisible by k.

Contains no semiprimes.

Examples

			a(3) = 66 is a term because 66 = 2*3*11 is not a prime or power of a prime and A341117(66) = 20262 = 66*307.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A341039, A341117.

Programs

Maple

f:= proc(n) local D, S,i;
  D:= sort(convert(numtheory:-divisors(n),list),`>`);
  S:= ListTools:-PartialSums(D);
  add(D[i]*S[-i],i=1..nops(D))
end proc:
select(t -> not isprime(t) and nops(numtheory:-factorset(t))>1 and f(t) mod t = 0, [$2..10000]);

PARI

f(n) = my(d=divisors(n)); sum(k=1, #d, d[k]*sum(i=#d-k+1, #d, d[i])); \\ A341117
isok(m) = !(isprimepower(m) || (m==1)) && !(f(m) % m); \\ Michel Marcus, Feb 05 2021