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 A372631 Numbers m for which there exists some k < m where the sum of the natural numbers from k^2 to m^2 inclusive is a square. 3
 4, 5, 7, 12, 15, 19, 29, 34, 41, 47, 55, 56, 65, 71, 73, 80, 84, 98, 111, 119, 124, 126, 141, 158, 165, 169, 175, 191, 209, 231, 239, 253, 260, 265, 287, 322, 335, 345, 352, 359, 369, 376, 403, 408, 425, 436, 444, 463, 465, 491, 505, 532, 542, 548, 587, 620 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..1301 Nicolay Avilov, Problem 1876. Segment of a natural series (in Russian). EXAMPLE 4 is a term because the sum of all natural numbers from 3^2 to 4^2 inclusive is 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 = 100 = 10^2. MATHEMATICA a={}; For[m=1, m<=620, m++, flag=0; tot=m^2*(m^2+1)/2; For[k=1, k= startvalue for m in count(max(startvalue, 2)): m2 = m**2 for k in diop_quadratic(m2*(m2+1)-x*(x-1)-2*y**2): if (r:=int(k[0]))

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Last modified September 8 05:22 EDT 2024. Contains 375751 sequences. (Running on oeis4.)