A366246 The number of infinitary divisors of n that are "Fermi-Dirac primes" (A050376) and terms of A366242.

0, 1, 1, 0, 1, 2, 1, 1, 0, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 0, 2, 1, 1, 1, 3, 1, 2, 2, 2, 2, 0, 1, 2, 2, 2, 1, 3, 1, 1, 1, 2, 1, 2, 0, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 1, 2, 2, 2, 2

Offset

1,6

Links

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

Formula

Additive with a(p^e) = A139351(e).

a(n) = A064547(n) - A366247(n).

a(n) = A064547(A366244(n)).

a(n) >= 0, with equality if and only if n is in A366243.

a(n) <= A064547(n), with equality if and only if n is in A366242.

Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B + C), where B is Mertens's constant (A077761) and C = Sum_{p prime} f(1/p) = -0.25705126777012995187..., where f(x) = - x + Sum_{k>=0} (x^(4^k)/(1+x^(4^k))).

Mathematica

s[0] = 0; s[n_] := s[n] = s[Floor[n/4]] + If[OddQ[Mod[n, 4]], 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%2 \\ after Charles R Greathouse IV at A139351
a(n) = vecsum(apply(s, factor(n)[, 2]));

Crossrefs

Cf. A050376, A064547, A077761, A139351, A366242, A366243, A366247.

Sequence in context: A373029 A125072 A162642 * A361205 A355827 A139146

Adjacent sequences: A366243 A366244 A366245 * A366247 A366248 A366249

Keyword

nonn,easy

Author

Amiram Eldar, Oct 05 2023

Status

approved