A336815 -id:A336815 - cp's OEIS frontend

A339612 Number of sets of distinct positive integers whose sum of squares is a square, the largest integer of a set is n.

1, 1, 1, 2, 1, 3, 2, 5, 9, 11, 32, 51, 113, 184, 364, 605, 1175, 2077, 3749, 7108, 12214, 23871, 42474, 82212, 153738, 288842, 555593, 1041563, 2016299, 3809565, 7302893, 13914139, 26591478, 50942383, 97411030, 186943685, 358286670, 689827822, 1326042612, 2558758426

Offset: 1

Ilya Gutkovskiy, Dec 09 2020

nonn

			a(10) = 11 sets: {10}, {1, 2, 4, 10}, {1, 2, 8, 10}, {2, 4, 7, 10}, {5, 6, 8, 10}, {1, 5, 7, 9, 10}, {3, 4, 6, 8, 10}, {1, 3, 4, 7, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {1, 2, 5, 7, 8, 9, 10} and {1, 2, 3, 4, 7, 8, 9, 10}.

Alois P. Heinz, Table of n, a(n) for n = 1..100

Cf. A000290, A126024, A336815.

a = lambda n: b(n-1, n*n, 1) # for b() in A336815
print([a(n) for n in range(1, 30)]) # Michael S. Branicky, Dec 10 2020

a(n) = A336815(n) - A336815(n-1).

a(24)-a(40) from Michael S. Branicky, Dec 09 2020

A378171 Number of subsets of the first n positive cubes whose sum is a positive cube.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 11, 12, 18, 23, 32, 42, 67, 99, 150, 247, 391, 635, 1098, 1865, 2927, 4932, 9109, 14825, 26926, 48452, 83758, 148387, 263258, 468595, 840912, 1559322, 2785642, 5146754, 9454946, 16756330, 31372080, 57754175, 105385375, 196773661, 368705288, 671572482

Offset: 1

Ilya Gutkovskiy, Nov 18 2024

nonn

			a(8) = 11 subsets: {1}, {8}, {27}, {64}, {125}, {216}, {343}, {512}, {1, 216, 512}, {27, 64, 125} and {1, 27, 64, 125, 512}.

Michael S. Branicky, Table of n, a(n) for n = 1..74

Cf. A000578, A126111, A336815, A339615, A378170.

from sympy import integer_nthroot
def is_cube(n): return integer_nthroot(n, 3)[1]
from functools import cache
@cache
def b(n, soc):
    if n == 0:
        if soc > 0 and is_cube(soc): return 1
        return 0
    return b(n-1, soc) + b(n-1, soc+n**3)
a = lambda n: b(n, 0)
print([a(n) for n in range(1, 30)]) # Michael S. Branicky, Nov 18 2024

a(25) and beyond from Michael S. Branicky, Nov 18 2024

cp's OEIS Frontend

A339612 Number of sets of distinct positive integers whose sum of squares is a square, the largest integer of a set is n.

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