cp's OEIS Frontend

A363368 Decimal expansion of Sum_{primes p} 1/(p*log(p)*log(log(p))).

%I A363368 #26 Jun 13 2023 11:38:40
%S A363368 1,9,0,6,9,7,3,8,4,8,0,3,4,9,5,4,4,1,7,7,8,7,5,7,9,6,6,9,6,5,1,9,6,4,
%T A363368 0,3,3,6,1,8,9,3,8,3,5,2,2,9,4,8,5,3,6,6,0,5,5,9,5,2,4,2,9,4,7,1,4,5,
%U A363368 6,7,8,3,1,2,9,2,5,2,2,4,4,1,0,9,2,3,1,8,7,1,9,4,1,3,3,4,1,6,4,8,2,2,4,2,3
%N A363368 Decimal expansion of Sum_{primes p} 1/(p*log(p)*log(log(p))).
%C A363368 Value computed and communicated by Bill Allombert and confirmed by Pascal Sebah.
%e A363368 1.9069738480349544...
%o A363368 (PARI) /* author Bill Allombert */
%o A363368 \p150
%o A363368 pz(x, ex=0)=
%o A363368 {
%o A363368 my(s=bitprecision(x));
%o A363368 my(B=s/real(polcoef(x, 0))+ex);
%o A363368 sum(n=1, B, my(a=moebius(n)); if(a!=0, a*log(zeta(n*x))/n));
%o A363368 }
%o A363368 my(P=primes([2, 61])); intnum(x=1, [oo, log(67)], (pz(x)-vecsum([p^-x|p<-P]))*intnum(s=0, [oo, 1], (x-1)^s/gamma(1+s))) + vecsum([1/p/log(p)/log(log(p))|p<-P])
%Y A363368 Cf. A077761, A086242, A137245, A138312, A221711, A303493, A319231, A319232, A354887, A354917, A354952, A361972, A362533.
%K A363368 nonn,cons
%O A363368 1,2
%A A363368 _Artur Jasinski_, Jun 11 2023