A348641 -id:A348641 - cp's OEIS frontend

A348640 Denominators of the remainders in the greedy Egyptian fraction representation of 1 with square denominators (A348626).

1, 4, 2, 4, 36, 36, 1764, 2352, 115248, 416333400, 107225418169800, 562904175532925098845000, 1857180475556752726157213892231405000, 424594887903818740281781489141947299544299873193026842805000, 27616236678198713245845367246922973802897093015095664467139174240964043973815461112656369429045000

Offset: 0

Max Alekseyev, Oct 26 2021

a(n) divides LCM( A348626(1), ..., A348626(n) )^2.

			The first few remainders are 1, 3/4, 1/2, 1/4, 5/36, 1/36, 13/1764, 1/2352, 1/115248, 11/416333400, ... - _N. J. A. Sloane_, Apr 21 2025

Cf. A000058, A348626, A348641 (numerators), A382719.

s=1; for(n=1, 20, print1(denominator(s), ", "); t=sqrtint(floor(1/s))+1; s-=1/t^2);

a(n) = denominator of 1 - Sum_{k=1..n} 1/A348626(k)^2.

A382719 Numerator of Sum_{i=1..n} 1/A348626(i)^2.

Original entry on oeis.org

0, 1, 1, 3, 31, 35, 1751, 2351, 115247, 416333389, 107225418168983, 562904175532925088592367, 1857180475556752726157213791943527783, 424594887903818740281781489141947299537771799837674380866823, 27616236678198713245845367246922973802897093015095664467076756280985616142084296233915021926355087

Offset: 0

N. J. A. Sloane, Apr 21 2025

The denominators are given in A348640.

			The first few fractions are 0, 1/4, 1/2, 3/4, 31/36, 35/36, 1751/1764, 2351/2352, 115247/115248, 416333389/416333400, ...

Cf. A348626, A348640, A348641.

a(n) = A348640(n) - A348641(n).

cp's OEIS Frontend

A348640 Denominators of the remainders in the greedy Egyptian fraction representation of 1 with square denominators (A348626).

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