%I A145853
%S A145853 1,2,4,6,8,12,16,18,24,32,36,48,54,60,64,72,96,108,120,128,144,162,180,
%T A145853 192,216,240,256,288,300,324,360,384,420,432,480,486,512,540,576,600,
%U A145853 648,720,768,840,864,900,960,972,1024,1080,1152,1200,1260,1296,1440
%N A145853 Numbers n such that n is a multiple of all integers smaller than the 
               biggest prime dividing n.
%C A145853 The definition "Numbers n that if n is a multiple of a number a, then 
               n is a multiple of all integers less than a" produces the finite 
               sequence 1, 2.
%C A145853 A007694 (numbers n such that phi(n) divides n) is a subsequence. [From 
               Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 23 2008]
%e A145853 30 does not qualify because it is divisible by prime number 5 but not 
               by 4 < 5. However, the fact that 32 is divisible by 4 but not by 
               3 < 4 does not disqualify 32 from being in this sequence because 
               4 is not prime.
%t A145853 a = {1}; For[n = 2, n < 2000, n++, b = FactorInteger[n][[ -1, 1]]; If[Length[Select[Range[b], 
               Mod[n, # ] == 0 &]] == b, AppendTo[a, n]]]; a [From Stefan Steinerberger 
               (stefan.steinerberger(AT)gmail.com), Oct 25 2008]
%o A145853 (MAGMA) [ n: n in [1..1450] | forall{ x: x in [2..p] | n mod x eq 0 } 
               where p is #f eq 0 select 1 else f[ #f][1] where f is Factorization(n) 
               ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 23 
               2008]
%Y A145853 Cf. A007694, A006530 (largest prime dividing n). [From Klaus Brockhaus 
               (klaus-brockhaus(AT)t-online.de), Oct 23 2008]
%Y A145853 Sequence in context: A055932 A140067 A067946 this_sequence A064527 A007694 
               A050622
%Y A145853 Adjacent sequences: A145850 A145851 A145852 this_sequence A145854 A145855 
               A145856
%K A145853 nonn
%O A145853 1,2
%A A145853 J. Lowell (jhbubby(AT)mindspring.com), Oct 21 2008
%E A145853 More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and 
               Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 23 
               2008
%E A145853 Better definition from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Oct 23 2008