

A124508


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


8



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

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)));


LINKS

R. 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.


MATHEMATICA

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


CROSSREFS

Cf. A007283, A000400, A003586, A005117.
Sequence in context: A205029 A255488 A247513 * A028317 A220435 A340512
Adjacent sequences: A124505 A124506 A124507 * A124509 A124510 A124511


KEYWORD

nonn,mult


AUTHOR

Reinhard Zumkeller, Nov 04 2006


STATUS

approved



