A354515 Numbers k such that m - gpf(m) = k has no solution m >= 2, gpf = A006530.

1, 4, 8, 12, 16, 18, 27, 32, 36, 48, 50, 54, 60, 64, 72, 80, 81, 84, 90, 96, 100, 108, 112, 125, 128, 132, 135, 144, 147, 150, 160, 162, 176, 180, 192, 196, 198, 200, 208, 210, 216, 224, 225, 234, 242, 243, 250, 252, 256, 270, 275, 280, 288, 294, 300, 306, 320, 324

Offset: 1

Author

Jianing Song, Aug 16 2022

Keywords

• nonn
• easy

Comments

Numbers k such that there is no prime p such that gpf(k+p) = p.

Numbers k such that there is no prime factor p of k such that k+p is p-smooth.

Examples

			12 is a term since the prime factors of 12 are 2,3, and we have gpf(12+2) != 2 and gpf(12+3) != 3.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..9826 (all terms <= 80000)

Crossrefs

Cf. A006530, A076563.

Indices of 0 in A354512. Complement of A354514.

Programs

PARI

gpf(n) = vecmax(factor(n)[, 1]);
isA354515(n) = if(n, my(f=factor(n)[, 1]); for(i=1, #f, if(gpf(n+f[i])==f[i], return(0))); 1, 0)