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
Examples
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.
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
Programs
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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
Formula
a(n) = n + 37 for n >= 92.