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

%I A366643 #8 Oct 16 2023 09:30:14
%S A366643 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,
%T A366643 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,
%U A366643 2,2,2,1,2,2,1,2,4,2,2,1,1,2,2,2,2,2,2
%N A366643 a(n) is the number of divisors of n that are coprime to the terms of A366642.
%H A366643 Amiram Eldar, <a href="/A366643/b366643.txt">Table of n, a(n) for n = 1..10000</a>
%F A366643 Multiplicative with a(p^e) = 1 if p is a term of A366642, and e+1 otherwise.
%F A366643 Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A000005(k) = 1/2.
%F A366643 Dirichlet g.f.: zeta(s)^2 * Product_{p in A366642} (1 - 1/p^s).
%F A366643 Sum_{k=1..n} a(k) ~ c * n * log(n), where c = Product_{p in A366642} (1 - 1/p) = 0.26485234983834588444... .
%t A366643 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]
%Y A366643 Cf. A000005, A001227, A035218, A366642.
%K A366643 nonn,easy,mult
%O A366643 1,7
%A A366643 _Amiram Eldar_, Oct 15 2023