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A322354 Greatest common divisor of product p and product (p+2), where p ranges over distinct prime divisors of n; a(n) = gcd(A007947(n), A166590(A007947(n))).

%I A322354 #10 Dec 16 2018 17:57:39
%S A322354 1,2,1,2,1,2,1,2,1,2,1,2,1,2,5,2,1,2,1,2,3,2,1,2,1,2,1,2,1,10,1,2,1,2,
%T A322354 7,2,1,2,3,2,1,6,1,2,5,2,1,2,1,2,1,2,1,2,1,2,3,2,1,10,1,2,3,2,5,2,1,2,
%U A322354 1,14,1,2,1,2,5,2,1,6,1,2,1,2,1,6,1,2,1,2,1,10,1,2,3,2,1,2,1,2,1,2,1,2,1,2,105
%N A322354 Greatest common divisor of product p and product (p+2), where p ranges over distinct prime divisors of n; a(n) = gcd(A007947(n), A166590(A007947(n))).
%H A322354 Antti Karttunen, <a href="/A322354/b322354.txt">Table of n, a(n) for n = 1..15015</a>
%H A322354 Antti Karttunen, <a href="/A322354/a322354.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A322354 a(n) = A322362(A007947(n)) = gcd(A007947(n), A166590(A007947(n))).
%F A322354 a(n) = A322356(n) * A322357(n).
%t A322354 f[n_] := If[n == 1, 1, Times @@ Power @@@ ({#[[1]] + 2, #[[2]]} & /@ FactorInteger[n])]; rad[n_] := Times @@ (First@# & /@ FactorInteger@n); a[n_] := GCD[rad[n], f[rad[n]]]; Array[a, 120] (* _Amiram Eldar_, Dec 16 2018 *)
%o A322354 (PARI)
%o A322354 A166590(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] += 2); factorback(f); };
%o A322354 A322362(n) = gcd(n, A166590(n));
%o A322354 A007947(n) = factorback(factorint(n)[, 1]);
%o A322354 A322354(n) = A322362(A007947(n));
%o A322354 \\ Alternatively as:
%o A322354 A322354(n) = gcd(A007947(n), A166590(A007947(n)));
%Y A322354 Cf. A007947, A166590, A322356, A322357, A322362.
%Y A322354 Cf. also A066086.
%K A322354 nonn
%O A322354 1,2
%A A322354 _Antti Karttunen_, Dec 16 2018