A354525 Numbers k such that A354512(k) = A001221(k).

1, 2, 3, 5, 6, 7, 9, 11, 13, 14, 15, 17, 19, 21, 23, 25, 29, 31, 33, 35, 37, 41, 43, 45, 47, 49, 51, 53, 55, 59, 61, 62, 67, 69, 71, 73, 77, 79, 83, 85, 89, 91, 93, 95, 97, 101, 103, 107, 109, 113, 115, 119, 121, 127, 131, 133, 137, 139, 141, 143, 145, 149, 151, 155, 157

Offset: 1

Author

Jianing Song, Aug 16 2022

Keywords

• nonn
• easy

Comments

Numbers k such that for every prime factor p of k we have gpf(k+p) = p, gpf = A006530.

Numbers k such that for every prime factor p of k, k+p is p-smooth.

If k is an even term, then k+2 is a power of 2, so k is of the form 2*(2^m-1). Those m for which 2*(2^m-1) is a term are listed in A354531.

Examples

			15 is a term since the prime factors of 15 are 3,5, and we have gpf(15+3) = 3 and gpf(15+5) = 5.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..8435 (all terms <= 50000)

Crossrefs

Cf. A001221, A354512, A006530, A354531, A354532, A354533, A354534.

Indices of 0 in A354527. Complement of A354526.

Programs

PARI

gpf(n) = vecmax(factor(n)[, 1]);
isA354525(n) = my(f=factor(n)[, 1]); for(i=1, #f, if(gpf(n+f[i])!=f[i], return(0))); 1