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A122376 Number of prime factors (counted with multiplicity) of the smallest number with exactly n divisors. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

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

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

Table of n, a(n) for n=1..82.

FORMULA

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

MATHEMATICA

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

CROSSREFS

Sequence in context: A113885 A113886 A220096 * A067240 A126080 A060681

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

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Last modified November 22 15:27 EST 2017. Contains 295089 sequences.