A276269 a(n) = n + the largest (if n is even), or the smallest (if n is odd) prime factor of n if n > 1; and a(1)=1.

1, 4, 6, 6, 10, 9, 14, 10, 12, 15, 22, 15, 26, 21, 18, 18, 34, 21, 38, 25, 24, 33, 46, 27, 30, 39, 30, 35, 58, 35, 62, 34, 36, 51, 40, 39, 74, 57, 42, 45, 82, 49, 86, 55, 48, 69, 94, 51, 56, 55, 54, 65, 106, 57, 60, 63, 60, 87, 118, 65, 122, 93, 66, 66, 70, 77, 134

Offset: 1

Author

Michel Marcus, Aug 26 2016

Keywords

• nonn

Comments

This is the underlying sequence for sequence A256393.

a(n) is never prime, since for n>1 it is alternatively divisible by A006530(n) then by A020639(n). This explains the existence of the sequences noted [p] in A256393 comments. There are also such [c] sequences where c is composite like for instance for c=8.

Crossrefs

Cf. A006530 (Gpf), A020639 (Lpf), A256393.

Programs

PARI

a(n) = if (n==1, 1, my(f = factor(n)); if (n % 2, n + f[1,1], n + f[#f~, 1]));