%I A094348
%S A094348 1,2,4,6,12,24,36,48,60,72,120,180,240,360,420,720,840,1260,1680,2520,
%T A094348 5040,7560,10080,15120,20160,25200,27720,30240,45360,50400,55440,83160,
%U A094348 110880,166320,221760,277200,332640,360360,498960,554400,665280,720720
%N A094348 Numbers n such that, for some numbers (j,k), j<=k, n is the smallest 
               positive multiple of j of the first k positive integers.
%C A094348 Includes all highly composite numbers (A002182) and least common multiples 
               of 1 through n (A003418). It would be interesting to know: 1) whether 
               or not all deeply composite numbers (A095848, which includes all 
               members of A003418) also belong to this sequence; 2) if 72 is the 
               only member of this sequence not also belonging to A002182 or A095848.
%C A094348 465585120 is the first member of A095848 that is not a member of this 
               sequence. The first members that belong to neither A002182 nor A095848 
               are 72, 30240, 64864800 and 1470268800. - David Wasserman (dwasserm(AT)earthlink.net), 
               Jun 28 2007
%H A094348 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A094348 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/
               Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</
               a>, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 
               1972, p. 844.
%H A094348 J. Britton, <a href="http://britton.disted.camosun.bc.ca/perfect/jbperfect.htm">
               Perfect Number Analyzer</a>
%H A094348 Wikipedia, <a href="http://en.wikipedia.org/wiki/Table_of_divisors">Table 
               of divisors</a>.
%e A094348 72 is a multiple of seven of the first nine positive integers (namely, 
               1, 2, 3, 4, 6, 8 and 9). It is the smallest positive integer for 
               which this is true.
%Y A094348 Cf. A096179.
%Y A094348 Cf. A003418, A002182, A002201, A072938, A106037, A002110.
%Y A094348 Sequence in context: A056795 A141420 A141551 this_sequence A002182 A077006 
               A004394
%Y A094348 Adjacent sequences: A094345 A094346 A094347 this_sequence A094349 A094350 
               A094351
%K A094348 nonn
%O A094348 1,2
%A A094348 Matthew Vandermast (ghodges14(AT)comcast.net), Jun 18 2004, Oct 12 2008
%E A094348 More terms from David Wasserman (dwasserm(AT)earthlink.net), Jun 28 2007