

A072963


In prime factorization of n replace all single (i.e., nontwin) primes with 1.


2



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
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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 p2 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: A327656 A098985 A327539 * A161955 A276234 A000265
Adjacent sequences: A072960 A072961 A072962 * A072964 A072965 A072966


KEYWORD

nonn,mult


AUTHOR

Reinhard Zumkeller, Aug 20 2002


STATUS

approved



