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

1,3

Comments

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

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A007510, A000040.

Sequence in context: A098985 A356168 A327539 * A161955 A276234 A000265

Adjacent sequences: A072960 A072961 A072962 * A072964 A072965 A072966

Keyword

nonn,mult

Author

Reinhard Zumkeller, Aug 20 2002

Status

approved