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

%I #40 Mar 12 2017 12:55:30

%S 1,1,1,1,1,691,1,3617,43867,283,131,103,657931,9349,1721,37,

%T 151628697551,26315271553053477373,154210205991661,137616929,

%U 1520097643918070802691,59,383799511,653,417202699,577,39409,113161,67,2003,157,1226592271,839,37,688531,3112655297839

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Kummer&#39;s_congruence">Kummer's congruences</a>

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

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

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

%e |A001067(10)| = 174611 = 283*617. So a(10) = 283.

%e |A001067(16)| = 7709321041217 = 37*683*305065927. So a(16) = 37.

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

%o (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

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

%K nonn

%O 1,6

%A _Seiichi Manyama_, Jan 20 2017

%E More terms from _Michel Marcus_, Jan 21 2017