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A366643
a(n) is the number of divisors of n that are coprime to the terms of A366642.
2
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
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
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Oct 15 2023
STATUS
approved