cp's OEIS Frontend

A327657 Number of divisors of n that are 1 or whose prime indices have a common divisor > 1.

%I A327657 #9 Dec 06 2021 03:06:36
%S A327657 1,1,2,1,2,2,2,1,3,2,2,2,2,2,3,1,2,3,2,2,4,2,2,2,3,2,4,2,2,3,2,1,3,2,
%T A327657 3,3,2,2,4,2,2,4,2,2,4,2,2,2,3,3,3,2,2,4,3,2,4,2,2,3,2,2,6,1,4,3,2,2,
%U A327657 3,3,2,3,2,2,4,2,3,4,2,2,5,2,2,4,3,2,4,2,2,4,4,2,3,2,3,2,2,3,4,3,2,3,2,2,5
%N A327657 Number of divisors of n that are 1 or whose prime indices have a common divisor > 1.
%C A327657 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. Numbers whose prime indices have a common divisor > 1 are listed in A318978.
%H A327657 Antti Karttunen, <a href="/A327657/b327657.txt">Table of n, a(n) for n = 1..20000</a>
%H A327657 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>
%H A327657 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A327657 a(n) = A000005(n) - A318979(n). - _Antti Karttunen_, Dec 05 2021
%e A327657 The divisors of 90 that are 1 or whose prime indices have a common divisor > 1 are {1, 3, 5, 9}, so a(90) = 4.
%t A327657 Table[Length[Select[Divisors[n],GCD@@PrimePi/@First/@FactorInteger[#]!=1&]],{n,100}]
%o A327657 (PARI) A327657(n) = sumdiv(n, d, (1==d)||(gcd(apply(x->primepi(x), factor(d)[, 1]))>1)); \\ _Antti Karttunen_, Dec 05 2021
%Y A327657 See link for additional cross-references.
%Y A327657 Cf. A000005, A056239, A112798, A281116, A289509, A318979, A327406, A327656.
%K A327657 nonn
%O A327657 1,3
%A A327657 _Gus Wiseman_, Sep 21 2019
%E A327657 Data section extended up to 105 terms by _Antti Karttunen_, Dec 05 2021