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

%I A322356 #10 Dec 16 2018 17:57:45
%S A322356 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,
%T A322356 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,
%U A322356 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
%N A322356 Product of such primes p that both p and p-2 divide n, and p-2 is also prime.
%C A322356 Product of those distinct greater twin primes (A006512) that divide n for which the corresponding lesser twin prime (A001359) also divides n.
%H A322356 Antti Karttunen, <a href="/A322356/b322356.txt">Table of n, a(n) for n = 1..15015</a>
%H A322356 Antti Karttunen, <a href="/A322356/a322356.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A322356 a(n) = A322354(n) / A322357(n).
%F A322356 A001221(a(n)) = A001222(a(n)) = A322358(n).
%e A322356 For n = 105 = 3*5*7, a(105) = 5*7 = 35.
%t A322356 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 *)
%o A322356 (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); };
%Y A322356 Cf. A001359, A006512, A322354, A322357, A322358.
%K A322356 nonn
%O A322356 1,15
%A A322356 _Antti Karttunen_, Dec 16 2018