%I #32 Feb 19 2024 01:57:54

%S 10,50,170,370,470,590,610,670,710,730,790,850,1010,1070,1270,1370,

%T 1390,1490,1630,1670,1850,1970,1990,2230,2270,2290,2570,2630,2690,

%U 2770,2830,2890,2950,3050,3070,3110,3130,3170,3310,3350,3470,3530

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

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

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

%H T. D. Noe, <a href="/A051230/b051230.txt">Table of n, a(n) for n = 1..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Von_Staudt%E2%80%93Clausen_theorem">Von Staudt-Clausen theorem</a>.

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers</a>.

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

%t 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 *)

%t Flatten[Position[BernoulliB[Range[4000]],_?(Denominator[#]==66&)]] (* _Harvey P. Dale_, Nov 17 2014 *)

%o (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 ]","))

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

%Y Equals 2*A051229.

%K nonn,nice,easy

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Michael Somos_

%E Name edited by _Petros Hadjicostas_, Jun 06 2020