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Search: id:A064538
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| A064538 |
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a(n) is the smallest number such that a(n)*(1^n + 2^n + ... + x^n) is a polynomial in x with integer coefficients. |
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3
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| 1, 2, 6, 4, 30, 12, 42, 24, 90, 20, 66, 24, 2730, 420, 90, 48, 510, 180, 3990, 840, 6930, 660, 690, 720, 13650, 1092, 378, 56, 870, 60, 14322, 7392, 117810, 7140, 210, 72, 1919190, 103740, 8190, 1680, 94710, 13860, 99330, 9240, 217350
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Note 80% of first 45 entries are adjacent to at least one prime number. [From Bill R McEachen (bmceache(AT)centralsan.org), Jan 26 2009]
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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. 804, Eq. 23.1.4.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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].
Dr. Math, summing n^k.
E. S. Rowland, Sums of Consecutive Powers
Eric Weisstein's World of Mathematics, Power Sum
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EXAMPLE
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1^3 + 2^3 + ... + x^3 = (x(x+1))^2/4 so a(3)=4.
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MAPLE
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A064538 := proc(n) local t1; t1 := eval((bernoulli(n+1, m+1)-bernoulli(n+1))/(n+1)); denominator(factor(t1)); end;
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CROSSREFS
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Sequence in context: A164020 A057643 A073039 this_sequence A002790 A108951 A108435
Adjacent sequences: A064535 A064536 A064537 this_sequence A064539 A064540 A064541
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 08 2001
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