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a(n) = the smallest positive integer non-coprime to both n and d(n), where d(n) is the number of divisors of n.
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%I #9 Feb 18 2023 08:08:37

%S 2,6,6,10,2,14,2,3,2,22,2,26,2,6,10,34,2,38,2,6,2,46,2,15,2,6,2,58,2,

%T 62,2,6,2,10,3,74,2,6,2,82,2,86,2,3,2,94,2,21,2,6,2,106,2,10,2,6,2,

%U 118,2,122,2,3,14,10,2,134,2,6,2,142,2,146,2,3,2,14,2,158,2,15,2,166,2,10,2,6

%N a(n) = the smallest positive integer non-coprime to both n and d(n), where d(n) is the number of divisors of n.

%H Antti Karttunen, <a href="/A141377/b141377.txt">Table of n, a(n) for n = 2..16385</a>

%F a(n) = A141327(n, A000005(n)).

%o (PARI) A141377(n) = { my(d=numdiv(n)); for(k=2,oo,if(gcd(k,n)>1 && gcd(k,d)>1, return(k))); }; \\ _Antti Karttunen_, Feb 18 2023

%Y Cf. A141327, A141378, A141379.

%K nonn

%O 2,1

%A _Leroy Quet_, Jun 28 2008

%E Extended by _Ray Chandler_, Jun 24 2009