A350674 -id:A350674 - cp's OEIS frontend

A350673 Square array read by antidiagonals T(n, k), n, k >= 0; T(n, k) is the sum of the elements of the intersection of the multisets of positive squares summing to n and k, respectively, obtained by the greedy algorithm.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 4, 1, 2, 1, 0, 0, 0, 2, 2, 4, 4, 2, 2, 0, 0, 0, 0, 0, 3, 4, 5, 4, 3, 0, 0, 0, 0, 1, 0, 0, 4, 5, 5, 4, 0, 0, 1, 0, 0, 1, 1, 0, 4, 5, 6, 5, 4, 0, 1, 1, 0

Offset: 0

Rémy Sigrist, Jan 10 2022

			Array T(n, k) begins:
  n\k|  0  1  2  3  4  5  6  7  8  9  10
  ---+----------------------------------
    0|  0  0  0  0  0  0  0  0  0  0   0
    1|  0  1  1  1  0  1  1  1  0  0   1
    2|  0  1  2  2  0  1  2  2  0  0   1
    3|  0  1  2  3  0  1  2  3  0  0   1
    4|  0  0  0  0  4  4  4  4  4  0   0
    5|  0  1  1  1  4  5  5  5  4  0   1
    6|  0  1  2  2  4  5  6  6  4  0   1
    7|  0  1  2  3  4  5  6  7  4  0   1
    8|  0  0  0  0  4  4  4  4  8  0   0
    9|  0  0  0  0  0  0  0  0  0  9   9
   10|  0  1  1  1  0  1  1  1  0  9  10

Rémy Sigrist, PARI program for A350673

Cf. A350674.

PARI
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See Links section.
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T(n, k) = T(k, n).
T(n, n) = n.
T(n, 0) = T(0, k) = 0.

A350698 Consider the positive squares summing to n as obtained by the greedy algorithm; a(n) is the least of these squares.

Original entry on oeis.org

1, 1, 1, 4, 1, 1, 1, 4, 9, 1, 1, 1, 4, 1, 1, 16, 1, 1, 1, 4, 1, 1, 1, 4, 25, 1, 1, 1, 4, 1, 1, 1, 4, 9, 1, 36, 1, 1, 1, 4, 1, 1, 1, 4, 9, 1, 1, 1, 49, 1, 1, 1, 4, 1, 1, 1, 4, 9, 1, 1, 1, 4, 1, 64, 1, 1, 1, 4, 1, 1, 1, 4, 9, 1, 1, 1, 4, 1, 1, 16, 81, 1, 1, 1

Offset: 1

Rémy Sigrist, Jan 12 2022

nonn

			For n = 13:
- 13 = 3^2 + 2^2,
- so a(13) = 2^2.

Cf. A053610, A350674.

a(n, e=2) = { my (r=0); while (n, r=sqrtnint(n, e); n-=r^e); r^e }

a(n^2) = n^2.

a(n) = A350674(n, A053610(n)).

cp's OEIS Frontend

A350673 Square array read by antidiagonals T(n, k), n, k >= 0; T(n, k) is the sum of the elements of the intersection of the multisets of positive squares summing to n and k, respectively, obtained by the greedy algorithm.

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