"Matematika je královnou věd - a teorie čísel je královnou matematiky." -- C. F. Gauss
Zdeňkův matematický koutek:-)

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» Program pro výpočet vlastních frekvencí 2-hm. tlumené soustavy
» Program pro vykresleni rady OEIS A294149, k=sigma(n)/(sigma(n)-n-1) v PHP Novinka

» Zvláštní multidokonalá čísla/Special multiperfect numbers, sigma(n)/n = k + X with integer k and rational X (Z01-Z24)
» Numbers n such that sigma(n)-tau(n) is a perfect number: 7, 21, 25, 29, 246, 286, 2688, 4062, 33550337 - OEIS no. A219036 (Z25)
» Numbers n such that sigma(n)/tau(n) is a perfect number: 11, 14, 15, 91, 92, 132, 140, 991, 1891, 3525 - OEIS no. A219179 (Z26)
» Numbers n such that sigma(n)*tau(n) is a perfect number: 2, 13, 3554677, 7339129, 8125441 - OEIS no. A219221 (Z27)
» Numbers n such that (sigma(n)-n)*(tau(n)-1) is a perfect number: 4, 169; a(3)>10^12 (Z28)
» Numbers n such that (sigma(n)-n)/(tau(n)-1) is a perfect number: 30, 121, 252, 8432, 982081 - OEIS no. A219223 (Z29)
» Numbers n for which n=(tau(n)-1)^k with integer k: 4, 16, 27, 3125, 3375, 65536, 823543, 3748096 - OEIS no. A219338 (Z30)
» Numbers n for which sigma(n)-n=tau(n)^k for some integer k>0: 4, 26, 56, 90, 122, 568, 2042, 8186, 32762 - OEIS no. A219668 (Z31)

» Graf vlastních dělitelů přirozených čísel 1 až 1.000.000 z GNUPLOT

» Numbers n such than there are three distinct triples (k, k+n, k+2n) of squares: 3360, 13440, 30240, 43680, 53760, 84000 - OEIS no. A222154 (Z32)
» Numbers n such than there are four distinct triples (k, k+n, k+2n) of squares: 1367520, 5470080, 12307680, 21880320 - OEIS no. A222155 (Z33)
» Numbers n such than there are five distinct triples (k, k+n, k+2n) of squares: 287327040, 294053760, 1149308160, 2585943360 - OEIS no. A214155 (Z34)
» Numbers n such than there are six distinct triples (k, k+n, k+2n) of squares: 258594336000, 1034377344000, 2327349024000 - OEIS no. A226858 (Z35)
» Numbers n such than there are seven distinct triples (k, k+n, k+2n) of squares: 12671122464000, 50684489856000, 114040102176000 - OEIS no. A226954 (Z36)
» Numbers n such that sigma(n)-n-1 is a perfect number: 8, 115, 187, 1375, 2455, 8143, 13543, 18261, 21103 - OEIS no. A293992 (Z37)
» Numbers k such that sigma(k)/(sigma(k)-k-1) is a positive integer: 15, 20, 35, 95, 104, 119, 143, 207, 209, 287, 319, 323, 377, 464, 527, 559, 650, 779, 899, 923, 989, 1007 - OEIS no. A294149 (Z38)
» Numbers k such that k - 2 | sigma(k): - OEIS no. A298563 (Z39) Novinka

» Program pro test grafiky v PHP


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Aktualizace: 8. 5. 2020

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