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

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, 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, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0

Offset

1,36

Comments

First differs from A101436 at n = 32.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Additive with a(p^e) = A139352(e).

a(n) = A064547(n) - A366246(n).

a(n) = A064547(A366245(n)).

a(n) >= 0, with equality if and only if n is in A366242.

a(n) <= A064547(n), with equality if and only if n is in A366243.

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))).

Mathematica

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]

Prog

(PARI) s(e) = if(e>3, s(e\4)) + e%4\2 \\ after Charles R Greathouse IV at A139352
a(n) = vecsum(apply(s, factor(n)[, 2]));

Crossrefs

Cf. A050376, A064547, A101436, A139352, A366242, A366243, A366246.

Sequence in context: A330023 A328891 A101436 * A374247 A369165 A056170

Adjacent sequences: A366244 A366245 A366246 * A366248 A366249 A366250

Keyword

nonn,easy

Author

Amiram Eldar, Oct 05 2023

Status

approved