A366309 The number of infinitary divisors of n that are terms of A366243.

1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1

Offset

1,4

Links

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

Formula

Multiplicative with a(p^e) = 2^A139352(e).

a(n) = 2^A366247(n).

a(n) = A037445(n)/A366308(n).

a(n) = A037445(A366245(n)).

a(n) >= 1, with equality if and only if n is in A366242.

a(n) <= A037445(n), with equality if and only if n is in A366243.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 - 1/p)*(1 + Sum_{k>=1} 2^A139352(k)/p^k) = 1.44736831993091923328... .

Mathematica

s[0] = 0; s[n_] := s[n] = s[Floor[n/4]] + If[Mod[n, 4] > 1, 1, 0]; f[p_, e_] := 2^s[e]; a[1] = 1; a[n_] := Times @@ 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) = vecprod(apply(x -> 2^s(x), factor(n)[, 2]));

Crossrefs

Cf. A037445, A139352, A366242, A366243, A366245, A366247, A366246, A366308.

Sequence in context: A378177 A194799 A291119 * A007424 A369163 A323308

Adjacent sequences: A366306 A366307 A366308 * A366310 A366311 A366312

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 06 2023

Status

approved