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A145853
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Numbers n such that n is a multiple of all integers smaller than the biggest prime dividing n.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The definition "Numbers n that if n is a multiple of a number a, then n is a multiple of all integers less than a" produces the finite sequence 1, 2.
A007694 (numbers n such that phi(n) divides n) is a subsequence. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 23 2008]
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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.
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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 [From Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 25 2008]
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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) ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 23 2008]
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CROSSREFS
| Cf. A007694, A006530 (largest prime dividing n). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 23 2008]
Sequence in context: A055932 A140067 A067946 * A064527 A007694 A050622
Adjacent sequences: A145850 A145851 A145852 * A145854 A145855 A145856
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KEYWORD
| nonn
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AUTHOR
| J. Lowell (jhbubby(AT)mindspring.com), Oct 21 2008
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EXTENSIONS
| More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 23 2008
Better definition from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 23 2008
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