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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A006519 A356166 A327405 * A087258 A333763 A076775

Adjacent sequences: A322359 A322360 A322361 * A322363 A322364 A322365

Keyword

nonn

Author

Antti Karttunen, Dec 05 2018

Status

approved