A275520 Least k such that n divides d(k^k) (d = A000005, k > 0).

1, 3, 2, 3, 8, 5, 6, 7, 4, 19, 10, 11, 12, 13, 14, 15, 25, 17, 9, 19, 20, 21, 22, 23, 8, 45, 26, 55, 28, 29, 30, 15, 49, 33, 34, 35, 18, 37, 38, 39, 20, 41, 42, 21, 14, 45, 46, 35, 6, 39, 25, 51, 52, 35, 54, 55, 28, 57, 58, 59, 60, 61, 62, 15, 12, 65, 66, 33, 68, 69, 70, 35, 24

Offset: 1

Author

Altug Alkan, Jul 31 2016

Keywords

• nonn
• look

Comments

If n > 1 and n-1 is squarefree, then a(n) <= n-1. # Robert Israel, Apr 11 2023

Examples

			a(5) = 8 because A000005(8^8) = 25 is divisible by 5.
		

Links

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

Crossrefs

Cf. A005179, A062319.

Programs

Maple

g:= proc(k) option remember;
    local F,t;
    F:= ifactors(k)[2];
    mul(t[2]*k+1,t=F);
end proc:
f:= proc(n) local k;
  for k from 1 do if g(k) mod n = 0 then return k fi od
end proc:
map(f, [$1..100]); # Robert Israel, Apr 11 2023

Mathematica

Table[k = 1; While[! Divisible[DivisorSigma[0, k^k], n], k++]; k, {n, 73}] (* Michael De Vlieger, Aug 02 2016 *)

PARI

a(n) = {my(k=1); while(numdiv(k^k) % n != 0, k++); k; }