cp's OEIS Frontend

A366247 The number of infinitary divisors of n that are "Fermi-Dirac primes" (A050376) and terms of A366243.

%I A366247 #9 Oct 06 2023 10:57:13
%S A366247 0,0,0,1,0,0,0,1,1,0,0,1,0,0,0,0,0,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,0,0,
%T A366247 0,2,0,0,0,1,0,0,0,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0,1,
%U A366247 0,0,0,2,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0
%N A366247 The number of infinitary divisors of n that are "Fermi-Dirac primes" (A050376) and terms of A366243.
%C A366247 First differs from A101436 at n = 32.
%H A366247 Amiram Eldar, <a href="/A366247/b366247.txt">Table of n, a(n) for n = 1..10000</a>
%F A366247 Additive with a(p^e) = A139352(e).
%F A366247 a(n) = A064547(n) - A366246(n).
%F A366247 a(n) = A064547(A366245(n)).
%F A366247 a(n) >= 0, with equality if and only if n is in A366242.
%F A366247 a(n) <= A064547(n), with equality if and only if n is in A366243.
%F A366247 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime} f(1/p) = 0.39310573826635831710..., where f(x) = Sum_{k>=0} (x^(2*4^k)/(1+x^(2*4^k))).
%t A366247 s[0] = 0; s[n_] := s[n] = s[Floor[n/4]] + If[Mod[n, 4] > 1, 1, 0]; f[p_, e_] := s[e]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A366247 (PARI) s(e) = if(e>3, s(e\4)) + e%4\2 \\ after _Charles R Greathouse IV_ at A139352
%o A366247 a(n) = vecsum(apply(s, factor(n)[, 2]));
%Y A366247 Cf. A050376, A064547, A101436, A139352, A366242, A366243, A366246.
%K A366247 nonn,easy
%O A366247 1,36
%A A366247 _Amiram Eldar_, Oct 05 2023