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

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Aug 20 2002

Keywords

• nonn
• mult

Comments

a(a(n)) = a(n).

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007510, A000040.

Programs

Mathematica

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 *)

Formula

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