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

Author

Reinhard Zumkeller, Feb 02 2003

Keywords

• nonn
• mult

Links

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

Crossrefs

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

Programs

Mathematica

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

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)<David A. Corneth, Sep 27 2018

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).