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 A072963 In prime factorization of n replace all single (i.e., non-twin) primes with 1. 2

%I

%S 1,1,3,1,5,3,7,1,9,5,11,3,13,7,15,1,17,9,19,5,21,11,1,3,25,13,27,7,29,

%T 15,31,1,33,17,35,9,1,19,39,5,41,21,43,11,45,1,1,3,49,25,51,13,1,27,

%U 55,7,57,29,59,15,61,31,63,1,65,33,1,17,3,35,71,9,73,1,75,19,77,39,1,5,81

%N In prime factorization of n replace all single (i.e., non-twin) primes with 1.

%C a(a(n)) = a(n).

%H Amiram Eldar, <a href="/A072963/b072963.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p) = (if p+2 or p-2 is prime then p else 1), p prime.

%e a(92) = a(2*2*23) = 1; a(93) = a(3*31) = 3*31 = 93.

%t f[p_, e_] := If[!Or @@ PrimeQ[p + {-2, 2}], 1, p^e]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 81] (* _Amiram Eldar_, Jan 10 2020 *)

%Y Cf. A007510, A000040.

%K nonn,mult

%O 1,3

%A _Reinhard Zumkeller_, Aug 20 2002

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Last modified January 29 11:06 EST 2023. Contains 359922 sequences. (Running on oeis4.)