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

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

Comments

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

Examples

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

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.

Crossrefs

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

Equals 2*A051229.

Programs

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 *)

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 ]","))

Extensions

More terms from Michael Somos

Name edited by Petros Hadjicostas, Jun 06 2020