A354527 a(n) = A001221(n) - A354512(n).

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, 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, 0, 2, 0, 2, 0, 1, 1, 1, 0, 1, 0, 2, 1, 1, 0, 3, 0, 1, 1, 1, 0, 3, 0

Offset: 1

Author

Jianing Song, Aug 16 2022

Keywords

• nonn
• easy

Comments

Number of distinct prime factors p of n such that gpf(n+p) != p, gpf = A006530.

Number of distinct prime factors p of n such that n+p is not p-smooth.

Examples

			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.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A354512, A006530.

Cf. A354525 (indices of 0), A354526 (indices of positive terms).

Programs

PARI

gpf(n) = vecmax(factor(n)[, 1]);
a(n) = my(f=factor(n)[, 1]); sum(i=1, #f, gpf(n+f[i])!=f[i])