but there is A005179 !!

[vdmcc]

Neil,

------------------ sorry, disregard this 'kluns' -------------
 %I A000001
 %S A000001
1,2,4,6,16,12,64,30,36,48,1024,60,4096,192,144,210,65536,180,262144,
 %T A000001
240,576,3072,4194304,420,1296,12288,900,960,268435456,720,1073741824,
 %U A000001 2310,9216,196608,5184,1260,68719476736,786432,36864,1680
 %N A000001 Least number with n divisors
 %R A000001
 %O A000001 1,2
 %K A000001 nonn
 %A A000001 Wouter Meeussen (w.meeussen.vdmcc at vandemoortele.be)
 %t A000001
(Times@@(Prime[Range[Length[#]]]^Reverse[#-1]))&@Flatten[FactorInteger[n]/.{
a_Integer,b_}:>Table[a,{b}]]
----------------------------------------------------------------
WRONG!, repeated powers should be treated by partitions
SINCE There is the A005179 entry in the table,
(MY CLEANING this UP will take a moment);

%I A005179 M1026
%S A005179
1,2,4,6,16,12,64,24,36,48,1024,60,4096,192,144,120,65536,180,262144,
%T A005179
240,576,3072,4194304,360,1296,12288,900,960,268435456,720,1073741824,840,921
6
%N A005179 Smallest number with exactly n divisors.
%R A005179 D1 1 52. AMM 75 725 1968. Robe92 86.
%D A005179 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical
Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and
various reprintings), p.840.
%O A005179 1,2
%A A005179 njas
%K A005179 nonn,nice
%Y A005179 Cf. A007416.
%D A005179 T. Verhoeff, Rectangular and Trapezoidal Arrangements, Technical
Note, (1998), 8 pages.
%H A005179 Technical Note
------------------------------------------------------------------
*** this is the good way ***
*** and with more terms ***

{1,2,4,6,16,12,64,24,36,48,1024,60,4096,192,144,120,65536,180,262144,240,576
,
  3072,4194304,360,1296,12288,900,960,268435456,720,1073741824,840,9216,
  196608,5184,1260,68719476736,786432,36864,1680,1099511627776,2880,
  4398046511104,15360,3600,12582912,70368744177664,2520,46656,6480,589824,

61440,4503599627370496,6300,82944,6720,2359296,805306368,288230376151711744,
  5040,1152921504606846976,3221225472,14400,7560}

using a longer %t line this time (too long for my taste):

w[n_Integer]:=Module[{b,e,t},{b,e}=Transpose[FactorInteger[n]];
t=Flatten[Outer[u,Sequence@@(Partitions/@e),1]]/.u[s__]:>Flatten[b^{s}];
First[Cases[#,Min[#]]&@((Times@@(Prime[Range[Length[#]]]^(-Sort[-#+1])))&
/@t)]]

anyone for a smarter program?


w.meeussen.vdmcc at vandemoortele.be
tel  +32 (0) 51 33 21 11
fax +32 (0) 51 33 21 75



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