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

Author

Lekraj Beedassy, Aug 30 2006

Keywords

• nonn

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)

Crossrefs

Cf. A001222, A005179, A130279.

Programs

Mathematica

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

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

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