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Search: id:A045619
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| A045619 |
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Numbers that are the products of 2 or more consecutive integers. |
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+0
10
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| 0, 2, 6, 12, 20, 24, 30, 42, 56, 60, 72, 90, 110, 120, 132, 156, 182, 210, 240, 272, 306, 336, 342, 360, 380, 420, 462, 504, 506, 552, 600, 650, 702, 720, 756, 812, 840, 870, 930, 990, 992, 1056, 1122, 1190, 1260, 1320, 1332, 1406, 1482, 1560, 1640, 1680
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Erdos and Selfridge proved that numbers of this kind can never be a perfect power (A001597). - T. D. Noe (noe(AT)sspectra.com), Oct 13 2002
Numbers of the form x!/y! with y+1 < x. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 20 2008
a(n)=A000142(A137911(n))/A000142(A137912(n)-1) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Febr 27 2008
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REFERENCES
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P. Erdos and J.L. Selfridge, The product of consecutive integers is never a power, Illinois Jour. Math. 19 (1975, 292-301.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
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MATHEMATICA
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maxNum = 1700; lst = {}; For[i = 1, i <= Sqrt[maxNum], i++, j = i + 1; prod = i*j; While[prod < maxNum, AppendTo[lst, prod]; j++; prod *= j]]; lst = Union[lst]
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CROSSREFS
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Cf. A001597.
Cf. A000142, A137895, A053625, A093449, A100933, A084720.
Cf. A137899, A137900.
Adjacent sequences: A045616 A045617 A045618 this_sequence A045620 A045621 A045622
Sequence in context: A061078 A067114 A102711 this_sequence A028690 A120344 A031426
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Erich Friedman (erich.friedman(AT)stetson.edu)
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Jul 20 2000
More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Febr 27 2008
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