A309542 Numbers k such that A001414(k^3+1) is divisible by k.

1, 2, 5, 7, 20, 24, 45, 54, 286, 1942, 30771000, 71149819, 106438598, 668274063

Offset

1,2

Comments

a(15) > 1.5*10^9. - Giovanni Resta, Aug 07 2019

Links

Table of n, a(n) for n=1..14.

Example

5 is a member because the prime factorization of 5^3+1=126 is 2*3^2*7 and 2+3+3+7=15 is divisible by 5.

Maple

filter:= proc(n) local F, t;
  F:= ifactors(n^3+1)[2];
  add(t[1]*t[2], t=F) mod n = 0
end proc:
select(f, [$1..10000]);

Mathematica

sopfr[n_] := Total[Times @@@ FactorInteger[n]];
okQ[n_] := Divisible[sopfr[n^3+1], n];
Select[Range[10^5], okQ] (* Jean-François Alcover, May 14 2023 *)

Crossrefs

Cf. A001414, A309534, A309544.

Sequence in context: A041583 A143915 A355597 * A327322 A160820 A158357

Adjacent sequences: A309539 A309540 A309541 * A309543 A309544 A309545

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Aug 06 2019

Extensions

a(11)-a(14) from Giovanni Resta, Aug 07 2019

Status

approved