A061228 a(1) = 2, a(n) = smallest number greater than n which is not coprime to n.

2, 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

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(2m) = 2m+2, a(p)= 2p if p is a prime.

a(n)= n + the smallest divisor (more than 1) of n.

a(p^k) = p^k + p if p is prime. - Robert Israel, Oct 21 2015

Example

a(9) = 12 as 10 and 11 are coprime to 9. a(11) = 22 as 11 is a prime.

Maple

for n from 1 to 150 do if n=1 then printf(`%d, `, 2); fi: for k from n+1 to 2*n do if igcd(n, k)>1 then printf(`%d, `, k); break; fi: od: od:
# alternative:
2, seq(t + min(numtheory:-factorset(t)), t = 2..1000); # Robert Israel, Oct 21 2015

Mathematica

Table[n+First@(First/@FactorInteger[n]), {n, 200}] (* Vladimir Joseph Stephan Orlovsky, Apr 08 2011 *)

Prog

(Haskell)
a061228 n = n + a020639 n  -- Reinhard Zumkeller, May 06 2015

Crossrefs

Cf. A046666, A064413. Equals A020639(n) + n.

Cf. A070229, A256393.

Sequence in context: A056942 A115947 A247653 * A070229 A248835 A053568

Adjacent sequences: A061225 A061226 A061227 * A061229 A061230 A061231

Keyword

nonn

Author

Amarnath Murthy, Apr 23 2001

Extensions

More terms from James A. Sellers, Apr 24 2001

Status

approved