cp's OEIS Frontend

A325975 a(n) = gcd(A325977(n), A325978(n)).

%I A325975 #13 Jun 06 2019 21:58:46
%S A325975 1,1,1,1,1,6,1,1,1,2,1,4,1,2,3,1,1,3,1,2,1,2,1,12,1,2,1,4,1,6,1,1,3,2,
%T A325975 1,1,1,2,1,2,1,6,1,4,3,2,1,4,1,1,3,2,1,6,1,8,1,2,1,12,1,2,1,1,1,6,1,2,
%U A325975 3,2,1,3,1,2,1,4,1,6,1,2,1,2,1,4,1,2,3,4,1,18,7,4,1,2,5,12,1,1,3,1,1,6,1,2,3
%N A325975 a(n) = gcd(A325977(n), A325978(n)).
%C A325975 See comments in A325979 and A325981.
%H A325975 Antti Karttunen, <a href="/A325975/b325975.txt">Table of n, a(n) for n = 1..65537</a>
%F A325975 a(n) = gcd(A325977(n), A325978(n)).
%F A325975 a(n) = (1/2)*gcd(A034460(n)+A325313(n), A325814(n)+A325314(n)).
%o A325975 (PARI)
%o A325975 A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
%o A325975 A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
%o A325975 A325313(n) = (A048250(n) - n);
%o A325975 A325314(n) = (n - A162296(n));
%o A325975 A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
%o A325975 A034460(n) = (A034448(n) - n);
%o A325975 A048146(n) = (sigma(n)-A034448(n));
%o A325975 A325814(n) = (n-A048146(n));
%o A325975 A325977(n) = ((A034460(n)+A325313(n))/2);
%o A325975 A325978(n) = ((A325314(n)+A325814(n))/2);
%o A325975 A325975(n) = gcd(A325977(n), A325978(n));
%o A325975 \\ Or alternatively, as:
%o A325975 A325975(n) = (1/2)*gcd((A034460(n)+A325313(n)),(A325814(n)+A325314(n)));
%Y A325975 Cf. A034460, A048107, A325313, A325314, A325814, A325973, A325974, A325977, A325978, A325979, A325981.
%Y A325975 Cf. also A009194, A325385, A325813, A326046, A326047, A326048, A326056, A326057, A326060, A326062.
%K A325975 nonn
%O A325975 1,6
%A A325975 _Antti Karttunen_, Jun 02 2019