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 A290505 Hypotenuses for which there exist exactly 19 distinct integer triangles. 24
 203125, 265625, 406250, 453125, 531250, 578125, 609375, 640625, 796875, 812500, 828125, 906250, 953125, 1062500, 1140625, 1156250, 1218750, 1281250, 1359375, 1390625, 1421875, 1515625, 1578125, 1593750, 1625000, 1656250, 1703125, 1734375, 1765625, 1812500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers whose square is decomposable in 19 different ways into the sum of two nonzero squares: these are those with exactly two distinct prime divisors of the form 4k+1 with one, and six respective multiplicities, or with only one prime divisor of this form with multiplicity nineteen. LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Hamdi Sahloul) FORMULA Terms are obtained by the products A004144(k)*A002144(p1)*A002144(p2)^6, or A004144(k)*A002144(p1)^19 for k, p1, p2 > 0 ordered by increasing values. EXAMPLE a(1) = 203125 = 5^6*13, a(5) = 531250 = 2*5^6*17, a(281) = 12796875 = 3^2*5^6*7*13. MATHEMATICA r[a_]:={b, c}/.{ToRules[Reduce[0

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Last modified May 23 18:13 EDT 2024. Contains 372765 sequences. (Running on oeis4.)