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 A232175 Least positive k such that n^3 + k^2 is a square, or 0 if there is no such k. 3
 0, 1, 3, 6, 10, 3, 21, 8, 36, 15, 55, 6, 78, 35, 15, 48, 136, 27, 171, 10, 42, 99, 253, 10, 300, 143, 81, 42, 406, 15, 465, 64, 88, 255, 35, 63, 666, 323, 91, 3, 820, 21, 903, 55, 66, 483, 1081, 48, 1176, 125, 85, 39, 1378, 81, 165, 28, 76, 783, 1711, 15, 1830, 899, 63 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Numbers n such that a(n) = n*(n-1)/2  appear to be A000430. n = 1 is the only number for which a(n) = 0. - T. D. Noe, Nov 21 2013 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..1000 from T. D. Noe). MATHEMATICA Join[{0}, Table[k = 1; While[! IntegerQ[Sqrt[n^3 + k^2]], k++]; k, {n, 2, 100}]] (* T. D. Noe, Nov 21 2013 *) PROG (Python) import math for n in range(77):    n3 = n*n*n    y=1 for k in range(1, 10000001):      sum = n3 + k*k      r = int(math.sqrt(sum))      if r*r == sum:        print str(k)+', ',        y=0        break    if y: print '-, ', (Python) from __future__ import division from sympy import divisors def A232175(n):     n3 = n**3     ds = divisors(n3)     for i in range(len(ds)//2-1, -1, -1):         x = ds[i]         y = n3//x         a, b = divmod(y-x, 2)         if not b:             return a     return 0 # Chai Wah Wu, Sep 12 2017 (PARI) a(n) = {k = 1; while (!issquare(n^3+k^2), k++); k; } \\ Michel Marcus, Nov 20 2013 CROSSREFS Cf. A000290, A000430, A000578, A038202, A055527, A232176. Sequence in context: A333611 A329153 A337771 * A065234 A333531 A082184 Adjacent sequences:  A232172 A232173 A232174 * A232176 A232177 A232178 KEYWORD nonn AUTHOR Alex Ratushnyak, Nov 19 2013 STATUS approved

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Last modified April 12 12:39 EDT 2021. Contains 342920 sequences. (Running on oeis4.)