%I #18 Aug 17 2022 05:07:40
%S 0,0,0,1,0,0,0,1,0,1,0,2,0,0,0,1,0,2,0,1,0,1,0,1,0,1,1,1,0,2,0,1,0,1,
%T 0,2,0,1,1,1,0,2,0,1,0,1,0,2,0,2,0,1,0,2,0,1,1,1,0,3,0,0,1,1,1,2,0,1,
%U 0,2,0,2,0,1,1,1,0,1,0,2,1,1,0,3,0,1,1,1,0,3,0
%N a(n) = A001221(n) - A354512(n).
%C Number of distinct prime factors p of n such that gpf(n+p) != p, gpf = A006530.
%C Number of distinct prime factors p of n such that n+p is not p-smooth.
%H Jianing Song, <a href="/A354527/b354527.txt">Table of n, a(n) for n = 1..10000</a>
%e a(30) = 2 since the prime factors of 30 are 2,3,5, and we have gpf(30+3) != 3 and gpf(30+5) != 5.
%o (PARI) gpf(n) = vecmax(factor(n)[, 1]);
%o a(n) = my(f=factor(n)[, 1]); sum(i=1, #f, gpf(n+f[i])!=f[i])
%Y Cf. A001221, A354512, A006530.
%Y Cf. A354525 (indices of 0), A354526 (indices of positive terms).
%K nonn,easy
%O 1,12
%A _Jianing Song_, Aug 16 2022