A079065 In prime factorization of n replace odd primes with 3.

1, 2, 3, 4, 3, 6, 3, 8, 9, 6, 3, 12, 3, 6, 9, 16, 3, 18, 3, 12, 9, 6, 3, 24, 9, 6, 27, 12, 3, 18, 3, 32, 9, 6, 9, 36, 3, 6, 9, 24, 3, 18, 3, 12, 27, 6, 3, 48, 9, 18, 9, 12, 3, 54, 9, 24, 9, 6, 3, 36, 3, 6, 27, 64, 9, 18, 3, 12, 9, 18, 3, 72, 3, 6, 27, 12, 9, 18, 3, 48, 81, 6, 3, 36, 9, 6, 9, 24, 3

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

Fully multiplicative with a(2) = 2, a(p) = 3 for odd primes p.

a(n) <= n; a(n)=n iff n is 3-smooth (A003586).

A065333(a(n)) = 1.

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

A001221(a(n)) <= A001221(n).

A001222(a(n)) = A001222(n).

A006519(a(n)) = A006519(n).

Mathematica

a[n_] := 3^(PrimeOmega[n] - (e = IntegerExponent[n, 2])) * 2^e; Array[a, 100] (* Amiram Eldar, Jul 13 2023 *)

Prog

(PARI) A079065(n) =  { my(f=factor(n)); for(i=1, #f~, if(f[i, 1]%2, f[i, 1] = 3)); factorback(f); }; \\ Antti Karttunen, Sep 27 2018
(PARI) a(n) = my(e2 = valuation(n, 2)); 3^(bigomega(n) - e2)<<e2 \\ David A. Corneth, Sep 27 2018

Crossrefs

Cf. A001221, A001222, A003586, A006519, A065333.

Sequence in context: A337532 A092089 A117659 * A097272 A126630 A167234

Adjacent sequences: A079062 A079063 A079064 * A079066 A079067 A079068

Keyword

nonn,mult

Author

Reinhard Zumkeller, Feb 02 2003

Status

approved