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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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2
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15, 315, 5040, 85680, 278460, 42840, 14608440, 540512280, 10810245600, 46844397600, 480155075400, 145486987846200, 17749412517236400, 5916470839078800, 10769949084069775600, 312328523438023492400
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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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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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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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