

A062757


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 161 = 15 qualifies as a term.


2



15, 315, 5040, 85680, 278460, 42840, 14608440, 540512280, 10810245600, 46844397600, 480155075400, 145486987846200, 17749412517236400, 5916470839078800, 10769949084069775600, 312328523438023492400
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OFFSET

1,1


REFERENCES

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. 216244.


LINKS

Table of n, a(n) for n=1..16.
L. Euler, Variae observationes circa series infinitas


EXAMPLE

a(2)=63 because the perfect square 64= 8^2 = 4^3.


MATHEMATICA

Table[ Denominator[ Plus@@(Take[ Select[ Range[ 2, 150 ], GCD@@(Last/@FactorInteger[ # ])>1& ]^21, k ]^1) ], {k, 1, 16} ]


CROSSREFS

Cf. A037450, A062834, A062965, A001597.
Sequence in context: A347980 A289951 A112489 * A088913 A053102 A327556
Adjacent sequences: A062754 A062755 A062756 * A062758 A062759 A062760


KEYWORD

nonn


AUTHOR

Jason Earls, Jul 16 2001


EXTENSIONS

More terms from Dean Hickerson, Jul 24, 2001


STATUS

approved



