A122376 Number of prime factors (counted with multiplicity) of the smallest number with exactly n divisors.

0, 1, 2, 2, 4, 3, 6, 4, 4, 5, 10, 4, 12, 7, 6, 5, 16, 5, 18, 6, 8, 11, 22, 6, 8, 13, 6, 8, 28, 7, 30, 6, 12, 17, 10, 6, 36, 19, 14, 7, 40, 9, 42, 12, 8, 23, 46, 7, 12, 9, 18, 14, 52, 7, 14, 9, 20, 29, 58, 8, 60, 31, 10, 8, 16, 13, 66, 18, 24, 11, 70, 9, 72, 37, 10, 20, 16, 15, 78, 9, 8, 41

Offset

1,3

Comments

This function is not additive; the smallest counterexample is a(40) = 7 != 4 + 4 = a(5) + a(8). - Franklin T. Adams-Watters Jul 10 2009

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 2000 terms from Amiram Eldar)

Formula

a(n) = Omega(A005179(n)), where Omega(n) = A001222(n).

a(p) = p-1 for prime p.

a(n) = A001222(A130279(n))/2. - Reinhard Zumkeller, May 21 2007

Mathematica

s = { (* terms in A005179 *) }; f[n_] := Plus @@ Last /@ FactorInteger@n; f /@ s (* Robert G. Wilson v, Aug 31 2006 *)

Crossrefs

Cf. A001222, A005179, A130279.

Sequence in context: A113886 A334952 A220096 * A067240 A126080 A302043

Adjacent sequences: A122373 A122374 A122375 * A122377 A122378 A122379

Keyword

nonn

Author

Lekraj Beedassy, Aug 30 2006

Extensions

More terms from Robert G. Wilson v, Aug 31 2006

Edited and extended by Ray Chandler, Sep 11 2006

Incorrect comment removed by Franklin T. Adams-Watters, Jul 11 2009

Status

approved