A154101 -id:A154101 - cp's OEIS frontend

A154100 Numbers n with property that n^2 are nonzero square terms in A077116.

2, 2, 9, 10, 7, 26, 37, 36, 30, 56, 26, 38, 145, 26, 170, 265, 208, 198, 130, 298, 73, 304, 135, 362, 208, 663, 730, 238, 767, 510, 704, 350, 915, 142, 584, 850, 369, 1090, 1090, 702, 730, 95, 1080, 1245, 97, 802, 1664, 738, 1090, 1971, 1904, 1276, 1295, 738, 1394

Offset: 1

Zak Seidov, Jan 04 2009

nonn

			2^2=4=A077116(2), 2^2=4=A077116(5), 9^2=81=A077116(13), 10^2=100=A077116(34).

Cf. A154101 corresponding indices of terms in A077116: 2,5,13,34,...

A233422 Numbers n such that m - n^3 is a square, where m is the least square above n^3.

Original entry on oeis.org

0, 2, 3, 6, 12, 20, 24, 30, 40, 42, 56, 60, 68, 75, 78, 84, 87, 120, 126, 160, 180, 248, 264, 270, 273, 308, 312, 318, 330, 336, 351, 360, 396, 564, 570, 588, 615, 620, 630, 635, 720, 738, 780, 840, 912, 1008, 1016, 1032, 1284, 1308, 1320, 1334, 1344, 1404, 1540, 1617

Offset: 1

Alex Ratushnyak, Dec 09 2013

nonn

Numbers n such that A070929(n) is a nonzero square.
The sequence of cubes a(n)^3 begins: 0, 8, 27, 216, 1728, 8000, 13824, 27000, 64000, 74088, 175616, 216000, 314432, ...
The sequence of m's begins: 1, 9, 36, 225, 1764, 8100, 13924, 27225, 64009, 74529, 176400, 216225, 314721, ...
The sequence of square roots of these m's begins: 1, 3, 6, 15, 42, 90, 118, 165, 253, 273, 420, 465, 561, 650, 689, 770, 812, ...
The sequence of squares m-n^3 begins: 1, 1, 9, 9, 36, 100, 100, 225, 9, 441, 784, 225, 289, 625, 169, 196, 841, ...
The sequence of their square roots begins: 1, 1, 3, 3, 6, 10, 10, 15, 3, 21, 28, 15, 17, 25, 13, 14, 29, 35, 43, 24, ... (note the first 12 terms are triangular numbers, A000217).

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A000290, A000578, A070929, A077115, A154101, A233400, A233401.

fQ[n_]:=Module[{c=n^3,m},m=(Floor[Sqrt[c]]+1)^2;IntegerQ[Sqrt[m-c]]];Select[Range[0,1650],fQ] (* Harvey P. Dale, Jan 03 2024 *)

is(n)=issquare((sqrtint(n=n^3)+1)^2-n) \\ Charles R Greathouse IV, Dec 09 2013

from math import isqrt
def isSquare(a):
  sr = isqrt(a)
  return (a==sr*sr)
for n in range(77777):
  n3 = n*n*n
  a = isqrt(n3)+1
  if isSquare(a*a-n3):  print(n, end=', ')

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A154100 Numbers n with property that n^2 are nonzero square terms in A077116.

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A233422 Numbers n such that m - n^3 is a square, where m is the least square above n^3.

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