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

1, 2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 54, 60, 64, 72, 96, 108, 120, 128, 144, 162, 180, 192, 216, 240, 256, 288, 300, 324, 360, 384, 420, 432, 480, 486, 512, 540, 576, 600, 648, 720, 768, 840, 864, 900, 960, 972, 1024, 1080, 1152, 1200, 1260, 1296, 1440

Offset: 1

Author

J. Lowell, Oct 21 2008

Keywords

• nonn

Comments

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.

A007694 (numbers m such that phi(m) divides m) is a subsequence. - Klaus Brockhaus, Oct 23 2008

Numbers m such that for p prime p|m => A003418(p)|m. - David W. Wilson, Jan 05 2019

Examples

			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.
		

Links

• David W. Wilson, Table of n, a(n) for n = 1..1000 (terms 1..200 from Vincenzo Librandi)

Crossrefs

Cf. A007694, A006530 (largest prime dividing n). - Klaus Brockhaus, Oct 23 2008

Programs

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

Mathematica

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 *)

Extensions

More terms from Klaus Brockhaus and Stefan Steinerberger, Oct 23 2008

Better definition from Stefan Steinerberger, Oct 23 2008