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
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
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]
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... .