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Search: id:A063008
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| A063008 |
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Canonical partition sequence (see A036036) encoded by prime factorization. The partition [P1+P2+P3+...] with P1>=P2>=P3>=... is encoded as 2^P1 * 3^P2 * 5^P3 *... |
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+0
5
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| 1, 2, 4, 6, 8, 12, 30, 16, 24, 36, 60, 210, 32, 48, 72, 120, 180, 420, 2310, 64, 96, 144, 240, 216, 360, 840, 900, 1260, 4620, 30030, 128, 192, 288, 480, 432, 720, 1680, 1080, 1800, 2520, 9240, 6300, 13860, 60060, 510510, 256, 384, 576, 960, 864, 1440, 3360
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Partitions are ordered first by sum. Then all partitions of n are viewed as exponent vectors on n variables and their corresponding monomials are ordered lexicographically. This gives a canonical ordering: [] [1] [2,0] [1,1] [3,0,0] [2,1,0] [1,1,1] [4,0,0,0] [3,1,0,0] [2,2,0,0] [2,1,1,0] [1,1,1,1]... Rearrangement of A025487, A036035 etc.
Or, least integer of each prime signature; resorted in accordance with the integer partitions described in A080577. - Alford Arnold (Alford1940(AT)aol.com), Feb 13 2008
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 831.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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EXAMPLE
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The sequence begins
1
2
4,6
8,12,30
16,24,36,60,210
32,48,72,120,180,420,2310
64,96,144,240,216,360,840,900,1260,4620,30030
Partition for n=17 is [2,1,1,1], so a(17)=2^2*3*5*7=420.
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CROSSREFS
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Cf. A025487 A080577.
Cf. A036036, A059901, A025487.
Sequence in context: A131885 A087443 A036035 this_sequence A059901 A136101 A086141
Adjacent sequences: A063005 A063006 A063007 this_sequence A063009 A063010 A063011
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KEYWORD
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nonn
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AUTHOR
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Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 02 2001
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EXTENSIONS
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Partially edited by N. J. A. Sloane (njas(AT)research.att.com), May 15, at the suggestion of R. J. Mathar
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