A323166 - OEIS

%I #9 Jan 09 2019 21:23:00

%S 1,1,1,1,1,6,1,1,1,2,1,4,1,2,3,1,1,6,1,10,1,2,1,12,1,2,1,4,1,6,1,1,3,

%T 2,1,2,1,2,1,2,1,6,1,4,15,2,1,4,1,2,3,2,1,6,1,8,1,2,1,60,1,2,1,1,1,6,

%U 1,2,3,2,1,18,1,2,1,4,1,6,1,2,1,2,1,4,1,2,3,4,1,90,7,4,1,2,5,12,1,2,3,10,1,6,1,2,3

%N Greatest common divisor of Product (1+(p_i^e_i)) and n, when n = Product (p_i^e_i); a(n) = gcd(A034448(n), n).

%H Antti Karttunen, <a href="/A323166/b323166.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A323166/a323166.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(n) = gcd(n, A034448(n)), where A034448 is usigma, the sum of unitary divisors of n.

%o (PARI)

%o A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448

%o A323166(n) = gcd(n, A034448(n));

%Y Cf. A034448, A323160, A323163.

%K nonn

%O 1,6

%A _Antti Karttunen_, Jan 09 2019