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 16-1 = 15 qualifies as a term.

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

Offset: 1

Author

Jason Earls, Jul 16 2001

Keywords

• nonn

Examples

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

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. 216-244.

Links

• L. Euler, Variae observationes circa series infinitas

Crossrefs

Cf. A037450, A062834, A062965, A001597.

Programs

Mathematica

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

Extensions

More terms from Dean Hickerson, Jul 24 2001