cp's OEIS Frontend

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

%I A275520 #20 Apr 12 2023 08:07:04
%S A275520 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,
%T A275520 26,55,28,29,30,15,49,33,34,35,18,37,38,39,20,41,42,21,14,45,46,35,6,
%U A275520 39,25,51,52,35,54,55,28,57,58,59,60,61,62,15,12,65,66,33,68,69,70,35,24
%N A275520 Least k such that n divides d(k^k) (d = A000005, k > 0).
%C A275520 If n > 1 and n-1 is squarefree, then a(n) <= n-1. # _Robert Israel_, Apr 11 2023
%H A275520 Robert Israel, <a href="/A275520/b275520.txt">Table of n, a(n) for n = 1..10000</a>
%e A275520 a(5) = 8 because A000005(8^8) = 25 is divisible by 5.
%p A275520 g:= proc(k) option remember;
%p A275520     local F,t;
%p A275520     F:= ifactors(k)[2];
%p A275520     mul(t[2]*k+1,t=F);
%p A275520 end proc:
%p A275520 f:= proc(n) local k;
%p A275520   for k from 1 do if g(k) mod n = 0 then return k fi od
%p A275520 end proc:
%p A275520 map(f, [$1..100]); # _Robert Israel_, Apr 11 2023
%t A275520 Table[k = 1; While[! Divisible[DivisorSigma[0, k^k], n], k++]; k, {n, 73}] (* _Michael De Vlieger_, Aug 02 2016 *)
%o A275520 (PARI) a(n) = {my(k=1); while(numdiv(k^k) % n != 0, k++); k; }
%Y A275520 Cf. A005179, A062319.
%K A275520 nonn,look
%O A275520 1,2
%A A275520 _Altug Alkan_, Jul 31 2016