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

%I A159475 #14 Sep 08 2022 08:45:43
%S A159475 1,4,6,6,10,8,14,10,12,12,22,14,26,16,18,18,34,20,38,22,24,24,46,26,
%T A159475 30,28,30,30,58,32,62,34,36,36,40,38,74,40,42,42,82,44,86,46,48,48,94,
%U A159475 50,56,52,54,54,106,56,60,58,60,60,118,62,122,64,66,66,70,68,134,70,72,72
%N A159475 a(1) = 1; for n >= 1, a(n) is the smallest number m > n such that gcd(n,m) > 1.
%C A159475 Essentially the same as A061228. [_R. J. Mathar_, Apr 16 2009]
%H A159475 Vincenzo Librandi, <a href="/A159475/b159475.txt">Table of n, a(n) for n = 1..10000</a>
%F A159475 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.
%F A159475 a(n) = n + A020639(n), for n > 1. - _Michel Marcus_, Dec 02 2018
%t A159475 f[n_]:= n + FactorInteger[n][[1, 1]]; Join[{1}, Array[f, 70, 2]] (* _Vincenzo Librandi_, Dec 02 2018 *)
%o A159475 (PARI) a(n) = if (n==1, 1, n+factor(n)[1,1]); \\ _Michel Marcus_, Dec 02 2018
%o A159475 (Magma) [1] cat [n + PrimeDivisors(n)[1]: n in [2..100]]; // _Vincenzo Librandi_, Dec 02 2018
%Y A159475 Cf. A000040, A020639, A061228.
%K A159475 nonn
%O A159475 1,2
%A A159475 _Jaroslav Krizek_, Apr 13 2009
%E A159475 More terms from _Michel Marcus_, Dec 02 2018