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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.
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%I #71 Jan 03 2021 15:52:41

%S 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 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 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 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 Positions of records: 0, 1, 8, 14, 35, 39, 65, 87, ...

%H Antti Karttunen, <a href="/A306709/b306709.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = gcd(sopfr(n), A003958(n)*A003959(n)) for n > 1; a(1) = 0.

%F a(p) = 1 for all primes p. - _Antti Karttunen_, Jan 03 2021

%o (PARI)

%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);

%o A167344(n) = { my(f=factor(n)); for(i=1,#f~,f[i,1] = (f[i,1]^2)-1); factorback(f); };

%o A306709(n) = if(1==n, 0, gcd(A001414(n), A167344(n))); \\ _Antti Karttunen_, Jan 03 2021

%Y Cf. A001414, A003958, A003959, A167344.

%K nonn,easy

%O 1,8

%A _Juri-Stepan Gerasimov_, May 20 2019