A061228 a(1) = 2, a(n) = smallest number greater than n that 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

Author

Amarnath Murthy, Apr 23 2001

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A020639, A046666, A064413, A087349.

Cf. A070229, A256393.

Programs

Haskell

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

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 *)
nxt[{n_,a_}]:=Module[{c=n+2},While[CoprimeQ[n+1,c],c++];{n+1,c}]; NestList[nxt,{1,2},70][[;;,2]] (* Harvey P. Dale, May 21 2025 *)

PARI

a(n) = n + if(n == 1, 1, factor(n)[1,1]); \\ Amiram Eldar, Apr 10 2025

Formula

a(n) = A020639(n) + n.

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

a(n) = n + the smallest divisor of n that is larger than 1, for n >= 2.

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

a(n) = A087349(n-1) + 1 for n >= 2. - Amiram Eldar, Apr 10 2025

Extensions

More terms from James Sellers, Apr 24 2001