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

1,2

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.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

f:= proc(n) if n::even then n + max(NumberTheory:-PrimeFactors(n)) else n + min(NumberTheory:-PrimeFactors(n)) fi end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Mar 26 2026

Prog

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

Crossrefs

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

Sequence in context: A155750 A159475 A098350 * A163173 A058640 A075653

Adjacent sequences: A276266 A276267 A276268 * A276270 A276271 A276272

Keyword

nonn,look

Author

Michel Marcus, Aug 26 2016

Status

approved