

A145853


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


1



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
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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 pm => 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: A140067 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



