A366643 a(n) is the number of divisors of n that are coprime to the terms of A366642.

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 4, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2

Offset

1,7

Links

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

Formula

Multiplicative with a(p^e) = 1 if p is a term of A366642, and e+1 otherwise.

Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A000005(k) = 1/2.

Dirichlet g.f.: zeta(s)^2 * Product_{p in A366642} (1 - 1/p^s).

Sum_{k=1..n} a(k) ~ c * n * log(n), where c = Product_{p in A366642} (1 - 1/p) = 0.26485234983834588444... .

Mathematica

seq[max_] := With[{ps = {2, 3, 5, 149, 10771}}, If[max <= Max[ps], f[p_, e_] := If[MemberQ[ps, p], 1, e + 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, max], Print["Add to ps more terms from A366642"]]]; seq[10^6]

Crossrefs

Cf. A000005, A001227, A035218, A366642.

Sequence in context: A352517 A347981 A065081 * A212185 A270928 A290257

Adjacent sequences: A366640 A366641 A366642 * A366644 A366645 A366646

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 15 2023

Status

approved