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A322356
Product of such primes p that both p and p-2 divide n, and p-2 is also prime.
7
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.
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 16 2018
STATUS
approved