A101750 Number of integers <= 10^n that are the sum of 2 distinct nonzero squares.

2, 29, 293, 2649, 23760, 215594, 1983334, 18451711, 173211045, 1637570777, 15570353488

Offset

1,1

Comments

Integers of the form m^2 + n^2 with m > n > 0 are given by A004431.

Links

Table of n, a(n) for n=1..11.

Example

a(2) = 29 because there are 29 terms in A004431 which are less than or equal to 100: {5, 10, 13, 17, 20, 25, 26, 29, 34, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 68, 73, 74, 80, 82, 85, 89, 90, 97, 100}

Mathematica

hyp = Union[ Flatten[ Table[ m^2 + n^2, {n, 2, 100000}, {m, n - 1}]]]; Table[ Length[ Select[ hyp, #<=10^n &]], {n, 8}]

Prog

(Python)
from math import isqrt
from itertools import combinations
def a(n):
    ub = 10**n
    sqs = [i**2 for i in range(1, isqrt(ub)+1)]
    return len(set(sum(c) for c in combinations(sqs, 2) if sum(c) <= ub))
print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Jun 19 2022

Crossrefs

Cf. A004431.

Sequence in context: A276196 A077023 A352065 * A160952 A088615 A091716

Adjacent sequences: A101747 A101748 A101749 * A101751 A101752 A101753

Keyword

nonn,more

Author

Robert G. Wilson v, Nov 09 2004

Extensions

Definition edited and a(7)-a(9) from Andrew Howroyd, Apr 14 2021

a(10)-a(11) from Michael S. Branicky, Jun 19 2022

Status

approved