A192336 Sums of two or more distinct squares.

5, 10, 13, 14, 17, 20, 21, 25, 26, 29, 30, 34, 35, 37, 38, 39, 40, 41, 42, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 68, 69, 70, 71, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Index entries for sequences related to sums of squares

Formula

a(n) = n + 37 for n >= 92.

Example

5 = 1^2 + 2^2 and 25 = 3^2 + 4^2 are members, but 2 = 1^2 + 1^2 and 36 = 6^2 are not.

Prog

(PARI) upto(lim)={
  my(x='x, A=prod(k=1, sqrt(lim), 1+x^(k^2), 1+O(x^floor(lim+1))), v=List());
  A-=sum(k=0, sqrt(lim), x^(k^2));
  for(n=5, lim, if(polcoeff(A, n), listput(v, n)));
  Vec(v)
};
(Python)
from itertools import combinations
def aupto(lim):
  s = [i*i for i in range(1, int(lim**.5)+2) if i*i <= lim]
  ss = set(sum(c) for i in range(2, len(s)+1) for c in combinations(s, i))
  return sorted(filter(lambda x: x <= lim, ss))
print(aupto(104)) # Michael S. Branicky, May 10 2021

Crossrefs

Complement of A028237; subset of A003995.

Sequence in context: A313376 A129846 A194464 * A001974 A242307 A313377

Adjacent sequences: A192333 A192334 A192335 * A192337 A192338 A192339

Keyword

nonn,easy

Author

Charles R Greathouse IV, Jun 28 2011

Status

approved