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

1,2

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A364157 A067946 A227270 * A318782 A064527 A333978

Adjacent sequences: A145850 A145851 A145852 * A145854 A145855 A145856

Keyword

nonn

Author

J. Lowell, Oct 21 2008

Extensions

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

Better definition from Stefan Steinerberger, Oct 23 2008

Status

approved