cp's OEIS Frontend

A306709 For n > 1, a(n) = gcd(A001414(n), A167344(n)) where A001414(n) is the sum of primes p dividing n (with repetition) and A167344(n) = b(n) is the totally multiplicative sequence with b(p) = (p-1)*(p+1) = p^2 - 1; a(1) = 0.

%I A306709 #71 Jan 03 2021 15:52:41
%S A306709 0,1,1,1,1,1,1,3,2,1,1,1,1,9,8,1,1,8,1,9,2,1,1,9,2,3,1,1,1,2,1,1,2,1,
%T A306709 12,2,1,3,16,1,1,12,1,15,1,1,1,1,2,12,4,1,1,1,16,1,2,1,1,12,1,3,1,3,
%U A306709 18,16,1,3,2,2,1,12,1,3,1,1,18,18,1,1,4,1,1,2,2,9,32,1,1,1,4,27
%N A306709 For n > 1, a(n) = gcd(A001414(n), A167344(n)) where A001414(n) is the sum of primes p dividing n (with repetition) and A167344(n) = b(n) is the totally multiplicative sequence with b(p) = (p-1)*(p+1) = p^2 - 1; a(1) = 0.
%C A306709 Positions of records: 0, 1, 8, 14, 35, 39, 65, 87, ...
%H A306709 Antti Karttunen, <a href="/A306709/b306709.txt">Table of n, a(n) for n = 1..65537</a>
%F A306709 a(n) = gcd(sopfr(n), A003958(n)*A003959(n)) for n > 1; a(1) = 0.
%F A306709 a(p) = 1 for all primes p. - _Antti Karttunen_, Jan 03 2021
%o A306709 (PARI)
%o A306709 A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);
%o A306709 A167344(n) = { my(f=factor(n)); for(i=1,#f~,f[i,1] = (f[i,1]^2)-1); factorback(f); };
%o A306709 A306709(n) = if(1==n, 0, gcd(A001414(n), A167344(n))); \\ _Antti Karttunen_, Jan 03 2021
%Y A306709 Cf. A001414, A003958, A003959, A167344.
%K A306709 nonn,easy
%O A306709 1,8
%A A306709 _Juri-Stepan Gerasimov_, May 20 2019