A119766 Numbers n such that numerator of Bernoulli(n)/n is (apart from sign) 1 or a prime.

1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 26, 34, 36, 38, 42, 74, 114, 118, 396, 674, 1870, 4306, 22808

Offset: 1

Author

N. J. A. Sloane, Jun 19 2006

Keywords

• nonn

Comments

In 1911 Ramanujan believed that the numerator of Bernoulli(n)/n for n even was (apart from sign) always either 1 or a prime. This is false.

Examples

			As an example, Bernoulli(20)/20 = -174611/6600, but 174611 = 283*617. - _Robert G. Wilson v_, Jun 22 2006
		

References

• S. Ramanujan, Some properties of Bernoulli's numbers, J. Indian Math. Soc., 3 (1911), 219-234.

Links

• K. Ono, Honoring a gift from Kumbakonam, Notices Amer. Math. Soc., 53 (2006), 640-651.

Crossrefs

Cf. A112548, A001067.

Programs

Maple

A119766 := proc(nmax) local numr; for n from 2 to nmax by 2 do numr := abs(numer(bernoulli(n)/n)) ; if numr = 1 or isprime(numr) then print(n) ; fi ; od ; end : A119766(2000) ; # R. J. Mathar, Jun 21 2006

Mathematica

OldPrimeQ[n_] := Abs[n]==1 || PrimeQ[Abs[n]]; Select[Range[2000], OldPrimeQ[Numerator[BernoulliB[ # ]/# ]] &] (* T. D. Noe, Jun 20 2006 *)

Extensions

a(21) and a(22) from T. D. Noe, Jun 20 2006