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Search: id:A062757
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| A062757 |
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Denominator of sum of first n terms of the series 1/15 + 1/63 + 1/80 ... in which the denominators are perfect squares - 1 which are simultaneously other powers, e.g. a(1) = 15 because 16 = 4^2 = 2^4, a perfect square that is also a fourth power; hence 16-1 = 15 qualifies as a term. |
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+0
3
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| 15, 315, 5040, 85680, 278460, 42840, 14608440, 540512280, 10810245600, 46844397600, 480155075400, 145486987846200, 17749412517236400, 5916470839078800, 10769949084069775600, 312328523438023492400
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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W. Dunham, Euler: The Master of Us All, The Mathematical Association of America, Washington D.C., 1999, p. 65.
L. Euler, "Variae observationes circa series infinitas," Opera Omnia, Ser. 1, Vol. 14, pp. 216-244.
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LINKS
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L. Euler, Variae observationes circa series infinitas
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EXAMPLE
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a(2)=63 because the perfect square 64= 8^2 = 4^3.
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MATHEMATICA
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Table[ Denominator[ Plus@@(Take[ Select[ Range[ 2, 150 ], GCD@@(Last/@FactorInteger[ # ])>1& ]^2-1, k ]^-1) ], {k, 1, 16} ]
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CROSSREFS
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Cf. A037450, A062834, A062965, A001597.
Sequence in context: A158533 A133766 A112489 this_sequence A088913 A053102 A132392
Adjacent sequences: A062754 A062755 A062756 this_sequence A062758 A062759 A062760
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KEYWORD
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nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Jul 16 2001
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EXTENSIONS
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More terms from Dean Hickerson (dean.hickerson(AT)yahoo.com), Jul 24, 2001
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