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

1,2

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.

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))).

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A205029 A255488 A247513 * A028317 A220435 A340512

Adjacent sequences: A124505 A124506 A124507 * A124509 A124510 A124511

Keyword

nonn,easy,mult

Author

Reinhard Zumkeller, Nov 04 2006

Status

approved