A037450 Numbers which are one less than a perfect square that cannot otherwise be written as a power.

3, 8, 24, 35, 48, 99, 120, 143, 168, 195, 224, 288, 323, 360, 399, 440, 483, 528, 575, 675, 783, 840, 899, 960, 1088, 1155, 1224, 1368, 1443, 1520, 1599, 1680, 1763, 1848, 1935, 2024, 2115, 2208, 2303, 2499, 2600, 2703, 2808, 2915, 3024, 3135

Offset: 1

Author

Jason Earls, Jul 21 2001

Keywords

• nonn

Comments

Denominators of decimal part of zeta(2) when it is represented as a sum of geometric series: zeta(2) = 1 + Sum_{n>=0} 1/a(n). - Andrés Ventas, Apr 06 2021

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
• Joakim Munkhammar, The Riemann zeta function as a sum of geometric series, The Mathematical Gazette (2020) Vol. 104, Issue 561, 527-530.

Crossrefs

Cf. A007916, A062834.

Programs

PARI

lista(m) = {for (i=2, m, sq = i^2; if (ispower(sq) == 2, print1(sq-1, ", ")););} \\ Michel Marcus, Apr 17 2013

Formula

a(n) = A007916(n)^2 - 1. - David A. Corneth, Apr 06 2021

Extensions

More terms from Dean Hickerson, Jul 24 2001

Offset corrected by Andrew Howroyd, Sep 18 2024