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

1,15

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..15015

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

Formula

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

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

Example

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

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 *)

Prog

(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); };

Crossrefs

Cf. A001359, A006512, A322354, A322357, A322358.

Sequence in context: A326073 A365490 A257098 * A337337 A119788 A334561

Adjacent sequences: A322353 A322354 A322355 * A322357 A322358 A322359

Keyword

nonn

Author

Antti Karttunen, Dec 16 2018

Status

approved