A159475 a(1) = 1; for n >= 1, a(n) is the smallest number m > n such that gcd(n,m) > 1.

1, 4, 6, 6, 10, 8, 14, 10, 12, 12, 22, 14, 26, 16, 18, 18, 34, 20, 38, 22, 24, 24, 46, 26, 30, 28, 30, 30, 58, 32, 62, 34, 36, 36, 40, 38, 74, 40, 42, 42, 82, 44, 86, 46, 48, 48, 94, 50, 56, 52, 54, 54, 106, 56, 60, 58, 60, 60, 118, 62, 122, 64, 66, 66, 70, 68, 134, 70, 72, 72

Offset: 1

Author

Jaroslav Krizek, Apr 13 2009

Keywords

• nonn

Comments

Essentially the same as A061228. [R. J. Mathar, Apr 16 2009]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A020639, A061228.

Programs

Magma

[1] cat [n + PrimeDivisors(n)[1]: n in [2..100]]; // Vincenzo Librandi, Dec 02 2018

Mathematica

f[n_]:= n + FactorInteger[n][[1, 1]]; Join[{1}, Array[f, 70, 2]] (* Vincenzo Librandi, Dec 02 2018 *)

PARI

a(n) = if (n==1, 1, n+factor(n)[1,1]); \\ Michel Marcus, Dec 02 2018

Formula

If n = Product (p_i^e_i), where p_1 < p_2 < ... < p_k, a(n) = n + p_1. For p = primes (A000040), a(p) = 2*p.

a(n) = n + A020639(n), for n > 1. - Michel Marcus, Dec 02 2018

Extensions

More terms from Michel Marcus, Dec 02 2018