cp's OEIS Frontend

A145853 Numbers m such that m is a multiple of all integers smaller than the largest prime dividing m.

%I A145853 #30 Sep 08 2022 08:45:38
%S A145853 1,2,4,6,8,12,16,18,24,32,36,48,54,60,64,72,96,108,120,128,144,162,
%T A145853 180,192,216,240,256,288,300,324,360,384,420,432,480,486,512,540,576,
%U A145853 600,648,720,768,840,864,900,960,972,1024,1080,1152,1200,1260,1296,1440
%N A145853 Numbers m such that m is a multiple of all integers smaller than the largest prime dividing m.
%C A145853 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 A145853 A007694 (numbers m such that phi(m) divides m) is a subsequence. - _Klaus Brockhaus_, Oct 23 2008
%C A145853 Numbers m such that for p prime p|m => A003418(p)|m. - _David W. Wilson_, Jan 05 2019
%H A145853 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 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 (* _Stefan Steinerberger_, 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) ]; // _Klaus Brockhaus_, Oct 23 2008
%Y A145853 Cf. A007694, A006530 (largest prime dividing n). - _Klaus Brockhaus_, Oct 23 2008
%K A145853 nonn
%O A145853 1,2
%A A145853 _J. Lowell_, Oct 21 2008
%E A145853 More terms from _Klaus Brockhaus_ and _Stefan Steinerberger_, Oct 23 2008
%E A145853 Better definition from _Stefan Steinerberger_, Oct 23 2008