A322356 - OEIS

%I #10 Dec 16 2018 17:57:45

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

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

%H Antti Karttunen, <a href="/A322356/b322356.txt">Table of n, a(n) for n = 1..15015</a>

%H Antti Karttunen, <a href="/A322356/a322356.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

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

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

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

%t 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 (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 Cf. A001359, A006512, A322354, A322357, A322358.

%K nonn

%O 1,15

%A _Antti Karttunen_, Dec 16 2018