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a(n) = gcd(n, A166590(n)), where A166590 is completely multiplicative with a(p) = p+2 for prime p.
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%I #12 Dec 05 2018 08:01:20

%S 1,2,1,4,1,2,1,8,1,2,1,4,1,2,5,16,1,2,1,4,3,2,1,8,1,2,1,4,1,10,1,32,1,

%T 2,7,4,1,2,3,8,1,6,1,4,5,2,1,16,1,2,1,4,1,2,1,8,3,2,1,20,1,2,9,64,5,2,

%U 1,4,1,14,1,8,1,2,5,4,1,6,1,16,1,2,1,12,1,2,1,8,1,10,1,4,3,2,1,32,1,2,1,4,1,2,1,8,105

%N a(n) = gcd(n, A166590(n)), where A166590 is completely multiplicative with a(p) = p+2 for prime p.

%H Antti Karttunen, <a href="/A322362/b322362.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A322362/a322362.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

%F a(n) = gcd(n, A166590(n)).

%F a(A037074(n)) = A006512(n).

%t a[n_] := If[n == 1, 1, GCD[n, Times@@ ((First[#]+2)^Last[#] &/@FactorInteger[n])]]; Array[a, 120] (* _Amiram Eldar_, Dec 05 2018~ *)

%o (PARI)

%o A166590(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] += 2); factorback(f); };

%o A322362(n) = gcd(n, A166590(n));

%Y Cf. A001359, A006512, A037074, A066086, A166590, A322361.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 05 2018