A062834 Denominator of sum of first n terms of the series 1/3 + 1/8 + 1/24 ... in which the denominators are one less than a perfect square that cannot otherwise be written as a power (cf. A062757, A037450).

3, 24, 2, 70, 1680, 55440, 55440, 65520, 65520, 5040, 10080, 5040, 1627920, 1627920, 85680, 942480, 21677040, 492660, 107100, 64260, 621180, 1242360, 1328040, 10624320, 1328040, 14608440, 1217370, 277560360, 133506533160

Offset: 1

Author

Jason Earls, Jul 21 2001

Keywords

• nonn

References

• W. Dunham, Euler: The Master of Us All, The Mathematical Association of America, Washington D.C., 1999, p. 66.
• 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. A062757, A037450.

Programs

Mathematica

Table[ Denominator[ Plus@@(Take[ Select[ Range[ 2, 50 ], GCD@@(Last/@FactorInteger[ # ])==1& ]^2-1, k ]^-1) ], {k, 1, 29} ]

Extensions

More terms from Dean Hickerson, Jul 24 2001