A281331 Smallest prime factor of |A001067(n)|, or 1 if |A001067(n)| = 1.

1, 1, 1, 1, 1, 691, 1, 3617, 43867, 283, 131, 103, 657931, 9349, 1721, 37, 151628697551, 26315271553053477373, 154210205991661, 137616929, 1520097643918070802691, 59, 383799511, 653, 417202699, 577, 39409, 113161, 67, 2003, 157, 1226592271, 839, 37, 688531, 3112655297839

Offset: 1

Author

Seiichi Manyama, Jan 20 2017

Keywords

• nonn

Examples

			|A001067(10)| = 174611 = 283*617. So a(10) = 283.
|A001067(16)| = 7709321041217 = 37*683*305065927. So a(16) = 37.
		

Links

• Wikipedia, Kummer's congruences

Crossrefs

Cf. A000928, A001067, A020639, A033563, A112548, A281332.

Programs

Mathematica

a[n_] := FactorInteger[Abs[Numerator[BernoulliB[2*n] / (2*n)]]][[1, 1]]; Table[a[n], {n, 1, 36}] (* Indranil Ghosh, Mar 12 2017 *)

PARI

a(n) = my(num = abs(numerator(bernfrac(2*n)/(2*n)))); if (num==1, 1, factor(num)[1,1]); \\ Michel Marcus, Jan 21 2017

Formula

a(n) = A020639(|A001067(n)|).

If n = A112548(m)/2, a(n) = |A001067(n)|.

a(18*m-2) = 37 for m > 0.

Extensions

More terms from Michel Marcus, Jan 21 2017