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A130024 a(1)=1. a(n) = number of earlier terms which don't have 2 or more distinct prime divisors in common with n.

%I A130024 #14 Oct 20 2024 21:00:06
%S A130024 1,1,2,3,4,5,6,7,8,9,10,10,12,13,14,15,16,15,18,17,20,21,22,20,24,25,
%T A130024 26,26,28,19,30,31,32,33,34,30,36,37,38,33,40,31,42,42,40,45,46,38,48,
%U A130024 41,50,49,52,43,54,51,56,57,58,38,60,61,59,63,64,50,66,66,68,53,70,57,72
%N A130024 a(1)=1. a(n) = number of earlier terms which don't have 2 or more distinct prime divisors in common with n.
%C A130024 If n is in A354144 then a(n) = n-1. - _Robert Israel_, Oct 20 2024
%H A130024 Robert Israel, <a href="/A130024/b130024.txt">Table of n, a(n) for n = 1..10000</a>
%e A130024 The distinct primes which divide 20 are 2 and 5. So a(20) is the number of earlier terms which are not divisible by at least 2 distinct primes dividing 20; i.e. are not divisible by both 2 and 5. Among the first 19 terms only a(11)=10 and a(12)=10 are divisible by both 2 and 5. There are 17 other earlier terms, so a(20)=17.
%p A130024 f:= proc(k,S) local t,s;
%p A130024    t:= 0:
%p A130024    for s in S do if k mod s = 0 then t:= t+1; if t = 2 then return 0 fi fi od;
%p A130024    1
%p A130024 end proc:
%p A130024 A[1]:= 1:
%p A130024 for n from 2 to 100 do
%p A130024    dn:= numtheory:-factorset(n);
%p A130024    A[n]:= add(f(A[k],dn),k=1..n-1)
%p A130024 od:
%p A130024 seq(A[i],i=1..100); # _Robert Israel_, Oct 20 2024
%Y A130024 Cf. A131232, A354144.
%K A130024 nonn,look
%O A130024 1,3
%A A130024 _Leroy Quet_, Jun 20 2007
%E A130024 More terms from _Joshua Zucker_, Jul 18 2007