A322356 Product of such primes p that both p and p-2 divide n, and p-2 is also prime.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 35

Offset: 1

Author

Antti Karttunen, Dec 16 2018

Keywords

• nonn

Comments

Product of those distinct greater twin primes (A006512) that divide n for which the corresponding lesser twin prime (A001359) also divides n.

Examples

			For n = 105 = 3*5*7, a(105) = 5*7 = 35.
		

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. A001359, A006512, A322354, A322357, A322358.

Programs

Mathematica

f[p_, n_] := If[PrimeQ[p + 2] && Divisible[n, p + 2], p + 2, 1]; a[n_] := Times @@ (f[#, n] & /@ FactorInteger[n][[;; , 1]]); Array[a, 120] (* Amiram Eldar, Dec 16 2018 *)

PARI

A322356(n) = { my(f = factor(n), m=1); for(i=1, #f~, if(isprime(f[i,1]+2)&&!(n%(f[i,1]+2)), m *= (f[i,1]+2))); (m); };

Formula

a(n) = A322354(n) / A322357(n).

A001221(a(n)) = A001222(a(n)) = A322358(n).