A322362 a(n) = gcd(n, A166590(n)), where A166590 is completely multiplicative with a(p) = p+2 for prime p.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Dec 05 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

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

Programs

Mathematica

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

PARI

A166590(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] += 2); factorback(f); };
A322362(n) = gcd(n, A166590(n));

Formula

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

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