A113636 In the sequence of positive integers add 1 to each nonprime number.

2, 2, 3, 5, 5, 7, 7, 9, 10, 11, 11, 13, 13, 15, 16, 17, 17, 19, 19, 21, 22, 23, 23, 25, 26, 27, 28, 29, 29, 31, 31, 33, 34, 35, 36, 37, 37, 39, 40, 41, 41, 43, 43, 45, 46, 47, 47, 49, 50, 51, 52, 53, 53, 55, 56, 57, 58, 59, 59, 61, 61, 63, 64, 65, 66, 67, 67, 69, 70, 71, 71, 73

Offset: 1

Author

Cino Hilliard, Jan 15 2006

Keywords

• easy
• nonn

Comments

This is the complement of sequence A014683.

Möbius transform of A380449(n). - Wesley Ivan Hurt, Jun 21 2025

Crossrefs

Cf. A005171, A014683, A014684, A113523, A113638, A179278, A380449.

Programs

Mathematica

Array[# + Boole[! PrimeQ@ #] &, 72] (* Michael De Vlieger, Nov 05 2020 *)

PARI

a(n) = if (!isprime(n), n+1, n); \\ Michel Marcus, Nov 06 2020

Formula

a(n) = A014684(n) + 1. - Bill McEachen, Nov 01 2020

From Wesley Ivan Hurt, Jun 21 2025: (Start)

a(n) = n + c(n), where c = A005171.

a(n) = Sum_{d|n} A380449(d) * mu(n/d). (End)

Extensions

Offset 1 from Michel Marcus, Nov 06 2020