A309534 Numbers k such that A001414(k^2+1) is divisible by k.

1, 5, 34, 610, 698870988, 1134903170

Offset

1,2

Comments

If A001519(i-1) and A001519(i+1) are prime (or 1), then since A001519(i)^2+1=A001519(i-1)*A001519(i+1) and A001519(i-1)+A001519(i+1)=3*A001519(i), A001519(i) is in the sequence. 1, 5, 34, 610 and 1134903170 arise in this way.

a(7) > 10^10. - Giovanni Resta, Aug 07 2019

Links

Table of n, a(n) for n=1..6.

Example

34 is a member because 34^2+1=13*89 and 13+89=3*34.

Maple

filter:= proc(n) local F, t, y;
  F:= ifactors(n^2+1)[2];
  y:= add(t[1]*t[2], t=F);
  y mod n = 0
end proc:
select(filter, [$1..10^6]);

Prog

(PARI) f(n) = (n=factor(n))[, 1]~*n[, 2]; \\ A001414
isok(k) = !(f(k^2+1) % k); \\ Michel Marcus, Aug 07 2019

Crossrefs

Cf. A001414, A001519.

Sequence in context: A211042 A086345 A295545 * A348375 A194687 A208098

Adjacent sequences: A309531 A309532 A309533 * A309535 A309536 A309537

Keyword

nonn,more

Author

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

Extensions

a(5)-a(6) from Giovanni Resta, Aug 07 2019

Status

approved