login
Greatest common divisor of n and the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).
8

%I #10 Jul 28 2022 21:16:07

%S 1,2,1,4,1,2,1,8,1,2,1,4,1,2,3,16,1,2,1,4,1,2,1,8,1,2,1,4,1,6,1,32,1,

%T 2,5,4,1,2,1,8,1,2,1,4,3,2,1,16,1,2,1,4,1,2,1,8,1,2,1,12,1,2,1,64,1,2,

%U 1,4,1,10,1,8,1,2,3,4,7,2,1,16,1,2,1,4,1,2,1,8,1,6,1,4,1,2,1,32,1,2,1,4,1,2,1,8,5

%N Greatest common divisor of n and the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).

%H Antti Karttunen, <a href="/A356166/b356166.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = gcd(n, A356164(n)) = gcd(n, A356165(n)) = gcd(A356164(n), A356165(n)).

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A356166(n) = for(k=1, oo, if((k*A003961(k))%n==0, return(gcd(n,k))));

%Y Cf. A003961, A191002, A356164, A356165, A356167, A356168, A356171 (positions of 1's), A356172.

%Y Cf. also A345992, A356151.

%K nonn,look

%O 1,2

%A _Antti Karttunen_, Jul 28 2022