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A323163 Greatest common divisor of product (1+(p^e)) and product p^(e-1), where p ranges over prime factors of n, with e corresponding exponent; a(n) = gcd(A034448(n), A003557(n)).

%I A323163 #7 Jan 09 2019 21:22:53
%S A323163 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,3,1,2,1,1,1,4,1,1,1,2,1,1,1,1,1,1,
%T A323163 1,2,1,1,1,2,1,1,1,2,3,1,1,4,1,1,1,2,1,3,1,4,1,1,1,2,1,1,1,1,1,1,1,2,
%U A323163 1,1,1,6,1,1,1,2,1,1,1,2,1,1,1,2,1,1,1,4,1,3,1,2,1,1,1,4,1,1,3,10,1,1,1,2,1
%N A323163 Greatest common divisor of product (1+(p^e)) and product p^(e-1), where p ranges over prime factors of n, with e corresponding exponent; a(n) = gcd(A034448(n), A003557(n)).
%H A323163 Antti Karttunen, <a href="/A323163/b323163.txt">Table of n, a(n) for n = 1..65537</a>
%F A323163 a(n) = gcd(A003557(n), A034448(n)).
%o A323163 (PARI)
%o A323163 A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
%o A323163 A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
%o A323163 A323163(n) = gcd(A003557(n), A034448(n));
%Y A323163 Cf. A003557, A034448, A322318, A323159.
%Y A323163 Differs from A062760 for the first time at n=36, where a(36) = 2, while A062760(36) = 1.
%K A323163 nonn
%O A323163 1,12
%A A323163 _Antti Karttunen_, Jan 09 2019