A051230 Numbers m such that the Bernoulli number B_m has denominator 66.

10, 50, 170, 370, 470, 590, 610, 670, 710, 730, 790, 850, 1010, 1070, 1270, 1370, 1390, 1490, 1630, 1670, 1850, 1970, 1990, 2230, 2270, 2290, 2570, 2630, 2690, 2770, 2830, 2890, 2950, 3050, 3070, 3110, 3130, 3170, 3310, 3350, 3470, 3530

Offset

1,1

Comments

From the von Staudt-Clausen theorem, denominator(B_{2*m}) = product of primes p such that (p-1)|2*m.

References

B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 75.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Wikipedia, Von Staudt-Clausen theorem.

Index entries for sequences related to Bernoulli numbers.

Example

The numbers m = 10, 50 belong to the list because B_10 = 5/66 and B_50 = 495057205241079648212477525/66. - Petros Hadjicostas, Jun 06 2020

Mathematica

denoBn[n_?EvenQ] := Times @@ Select[Prime /@ Range[PrimePi[n] + 1], Divisible[n, # - 1] & ]; Select[ Range[10, 4000, 10], denoBn[#] == 66 &] (* Jean-François Alcover, Jun 27 2012, after comments *)
Flatten[Position[BernoulliB[Range[4000]], _?(Denominator[#]==66&)]] (* Harvey P. Dale, Nov 17 2014 *)

Prog

(PARI) /* define indicator function */ a(n)=local(s); s=0; fordiv(n, d, s+=isprime(d+1)&(d>2)&(d!=10)); !s /* get sequence */ an=vector(45, n, 0); m=0; forstep(n=10, 4000, 10, if(a(n), an[ m++ ]=n)); for(n=1, 42, print1(an[ n ]", "))

Crossrefs

Cf. A045979, A051222, A051225, A051226, A051227, A051228.

Equals 2*A051229.

Sequence in context: A196507 A008531 A337732 * A008413 A006542 A237655

Adjacent sequences: A051227 A051228 A051229 * A051231 A051232 A051233

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from Michael Somos

Name edited by Petros Hadjicostas, Jun 06 2020

Status

approved