A124508 a(n) = 2^BigO(n) * 3^omega(n), where BigO = A001222 and omega = A001221, the numbers of prime factors of n with and without repetitions.

1, 6, 6, 12, 6, 36, 6, 24, 12, 36, 6, 72, 6, 36, 36, 48, 6, 72, 6, 72, 36, 36, 6, 144, 12, 36, 24, 72, 6, 216, 6, 96, 36, 36, 36, 144, 6, 36, 36, 144, 6, 216, 6, 72, 72, 36, 6, 288, 12, 72, 36, 72, 6, 144, 36, 144, 36, 36, 6, 432, 6, 36, 72, 192, 36, 216, 6, 72, 36, 216, 6, 288, 6

Offset: 1

Author

Reinhard Zumkeller, Nov 04 2006

Keywords

• nonn
• easy
• mult

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Prime Factorization.
• Eric Weisstein's World of Mathematics, Smooth number.

Crossrefs

Cf. A000079, A000244, A000400, A001221, A001222, A003586, A005117, A007283, A061142, A074816, A124509, A124510, A124511, A124512.

Programs

Mathematica

Table[2^PrimeOmega[n] 3^PrimeNu[n],{n,80}] (* Harvey P. Dale, Mar 26 2013 *)

PARI

a(n) = my(f = factor(n)); 2^bigomega(f) * 3^omega(f); \\ Amiram Eldar, Jul 11 2023

Formula

Multiplicative with p^e -> 3*2^e, p prime and e>0.

a(n) = A061142(n)*A074816(n) = A000079(A001222(n))*A000244(A001221(n)).

A124509 gives the range: A124509(n) = a(A124510(n)) and a(m) <> a(A124510(n)) for m < A124510(n).

For primes p, q with p <> q: a(p) = 6; a(p*q) = 36; a(p^k) = 3*2^k, k>0.

For squarefree numbers m: a(m) = 6^omega(m).

A001222(a(n)) = A001222(n)+1; A001221(a(n)) = 2 for n > 1.

A124511(n) = a(a(n)); A124512(n) = a(a(a(n))).