A348640
Denominators of the remainders in the greedy Egyptian fraction representation of 1 with square denominators (A348626).
Original entry on oeis.org
1, 4, 2, 4, 36, 36, 1764, 2352, 115248, 416333400, 107225418169800, 562904175532925098845000, 1857180475556752726157213892231405000, 424594887903818740281781489141947299544299873193026842805000, 27616236678198713245845367246922973802897093015095664467139174240964043973815461112656369429045000
Offset: 0
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
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s=1; for(n=1, 20, print1(denominator(s), ", "); t=sqrtint(floor(1/s))+1; s-=1/t^2);
A348641
Numerators of the remainders in the greedy Egyptian fraction representation of 1 with square denominators (A348626).
Original entry on oeis.org
1, 3, 1, 1, 5, 1, 13, 1, 1, 11, 817, 10252633, 100287877217, 6528073355352461938177, 62417959978427831731164878741347502689913, 70288410375198910851231147751405037331087262102769745506188780420713, 1637848790982120651632223869737258212156187623721099799629950249330321081907360495884020503587938103781073751577
Offset: 0
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
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s=1; for(n=1, 20, print1(numerator(s), ", "); t=sqrtint(floor(1/s))+1; s-=1/t^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
The first few fractions are 0, 1/4, 1/2, 3/4, 31/36, 35/36, 1751/1764, 2351/2352, 115247/115248, 416333389/416333400, ...
A348625
Number of Egyptian fractions with squared denominators: number of solutions to the equation 1 = 1/x_1^2 + ... + 1/x_n^2 with 0 < x_1 <= ... <= x_n.
Original entry on oeis.org
1, 0, 0, 1, 0, 1, 1, 4, 7, 47, 186, 1809, 27883
Offset: 1
A369607
Greedy solution a(1) < a(2) < ... to 1/a(1) + 1/a(2) + ... = (1 - 1/a(1)) * (1 - 1/a(2)) * ....
Original entry on oeis.org
3, 6, 29, 803, 643727, 414383582243, 171713753231982206218247, 29485613049014079571725771288849499850026859243, 869401376876189366008603664962520703088459987798626788985159595026678611496977754082506135887
Offset: 1
Showing 1-5 of 5 results.
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