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%I #13 Apr 30 2022 22:51:04
%S 1,1,1,1,1,6,1,1,1,2,1,12,1,2,3,1,1,6,1,2,1,2,1,12,1,2,1,4,1,6,1,1,3,
%T 2,1,36,1,2,1,2,1,6,1,4,3,2,1,12,1,2,3,2,1,6,1,8,1,2,1,12,1,2,1,1,1,6,
%U 1,2,3,2,1,72,1,2,3,4,1,6,1,2,1,2,1,12,1,2,3,4,1,18,7,4,1,2,5,12,1,2,3,4,1,6,1,2,3
%N a(n) = gcd(n, A003959(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e.
%H Antti Karttunen, <a href="/A348929/b348929.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = gcd(n, A003959(n)) = gcd(n, A348507(n)) = gcd(A003959(n), A348507(n)).
%t f[p_, e_] := (p + 1)^e; a[n_] := GCD[n, Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* _Amiram Eldar_, Nov 07 2021 *)
%o (PARI)
%o A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
%o A348929(n) = gcd(n, A003959(n));
%Y Cf. A003959, A085731, A126865, A323166, A348507, A348928, A348999 [= a(A276086(n))].
%Y Differs from similar A126795 for the first time at n=36, where a(36) = 36, while A126795(36) = 12.
%K nonn,easy,look
%O 1,6
%A _Antti Karttunen_, Nov 07 2021
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