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))).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Dec 16 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..15015
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A007947, A166590, A322356, A322357, A322362.

Cf. also A066086.

Programs

Mathematica

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 *)

PARI

A166590(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] += 2); factorback(f); };
A322362(n) = gcd(n, A166590(n));
A007947(n) = factorback(factorint(n)[, 1]);
A322354(n) = A322362(A007947(n));
\\ Alternatively as:
A322354(n) = gcd(A007947(n), A166590(A007947(n)));

Formula

a(n) = A322362(A007947(n)) = gcd(A007947(n), A166590(A007947(n))).

a(n) = A322356(n) * A322357(n).