A124970 Smallest positive integer which can be expressed as the ordered sum of 3 squares in exactly n different ways.

7, 1, 9, 41, 81, 146, 194, 306, 369, 425, 594, 689, 866, 1109, 1161, 1154, 1361, 1634, 1781, 1889, 2141, 2729, 2609, 3626, 3366, 3566, 3449, 3506, 4241, 4289, 4826, 5066, 5381, 7034, 5561, 6254, 7229, 7829, 8186, 8069, 8126, 8609, 8921, 8774, 10386, 11574, 11129

Offset

0,1

Links

Michael S. Branicky, Table of n, a(n) for n = 0..2102

Mathematica

f[n_] := Block[{k = 1}, While[Length@PowersRepresentations[k, 3, 2] != n, k++]; k]; Table[f[n], {n, 0, 44}] (* Ray Chandler, Oct 31 2019 *)

Prog

(Python)
from collections import Counter
from itertools import count, combinations_with_replacement as mc
def aupto(lim):
  sq = filter(lambda x: x<=lim, (i**2 for i in range(int(lim**(1/2))+2)))
  s3 = filter(lambda x: 0<x<=lim, (sum(m) for m in mc(sq, 3)))
  counts, alst = Counter(s3), [7]
  for n in count(1):
      mink = min((k for k in counts if counts[k]==n), default=False)
      if not mink: break
      alst.append(mink)
  return alst
print(aupto(11600)) # Michael S. Branicky, Jul 01 2021

Crossrefs

Cf. A000451, A095809, A000437, A122699, A124966-A124971.

Sequence in context: A349580 A197019 A048835 * A251768 A338561 A349140

Adjacent sequences: A124967 A124968 A124969 * A124971 A124972 A124973

Keyword

nonn

Author

Artur Jasinski, Nov 14 2006, Nov 20 2006

Extensions

Extended by Ray Chandler, Nov 30 2006

a(45) and beyond from Michael S. Branicky, Jul 01 2021

Status

approved