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Numbers m such that m is a multiple of all integers smaller than the largest prime dividing m.
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%I #30 Sep 08 2022 08:45:38

%S 1,2,4,6,8,12,16,18,24,32,36,48,54,60,64,72,96,108,120,128,144,162,

%T 180,192,216,240,256,288,300,324,360,384,420,432,480,486,512,540,576,

%U 600,648,720,768,840,864,900,960,972,1024,1080,1152,1200,1260,1296,1440

%N Numbers m such that m is a multiple of all integers smaller than the largest prime dividing m.

%C The definition "Numbers m such that if m is a multiple of a number k, then m is a multiple of all integers less than k" produces the finite sequence 1, 2.

%C A007694 (numbers m such that phi(m) divides m) is a subsequence. - _Klaus Brockhaus_, Oct 23 2008

%C Numbers m such that for p prime p|m => A003418(p)|m. - _David W. Wilson_, Jan 05 2019

%H David W. Wilson, <a href="/A145853/b145853.txt">Table of n, a(n) for n = 1..1000 </a> (terms 1..200 from Vincenzo Librandi)

%e 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 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 (* _Stefan Steinerberger_, Oct 25 2008 *)

%o (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) ]; // _Klaus Brockhaus_, Oct 23 2008

%Y Cf. A007694, A006530 (largest prime dividing n). - _Klaus Brockhaus_, Oct 23 2008

%K nonn

%O 1,2

%A _J. Lowell_, Oct 21 2008

%E More terms from _Klaus Brockhaus_ and _Stefan Steinerberger_, Oct 23 2008

%E Better definition from _Stefan Steinerberger_, Oct 23 2008