A097563 Least integer that can be written as a sum of zero or more distinct squares in exactly n ways, or -1 if no such number exists.

2, 0, 25, 50, 65, 94, 90, 110, 155, 126, 191, 170, 186, 174, 190, 211, 195, 226, 210, 231, 234, 235, 332, 255, 283, 259, 274, 275, 270, 323, 310, 286, 306, 299, 330, 381, 295, 347, 334, 319, 315, 331, 405, 339, 335, 364, 359, 351, 367, 387, 371, 370, 404, 438

Offset: 0

Author

Isabel C. Lugo (izzycat(AT)gmail.com), Aug 27 2004

Keywords

• easy
• sign

Comments

a(n) = -1 for almost all n. Conjecture: for n > 34189857569982621, this sequence is the integers > 37163, in order, interspersed with -1s. - Charles R Greathouse IV, Sep 04 2015

Examples

			a(4) = 65 because we can write 65 as a sum of distinct squares in four ways: 65 = 8^2 + 1^2 = 7^2 + 4^2 = 6^2 + 5^2 + 2^2 = 6^2 + 4^2 + 3^2 + 2^2 and we cannot do this with any smaller integer.
a(0) = 2 because we cannot write 2 as a sum of distinct squares and it is the smallest number with this property.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Crossrefs

First occurrence of n in A033461; see also A001422 (0 ways) and A003995 (1 or more ways).

Programs

Maple

gf := product(1+x^F(k), k=1..31); ser := series(gf, x=0, 1001); S := [seq(coeff(ser,x^(1*i)),i=1..1000)]; A := proc(i); x := 0; for j from 1 to nops(a) while x = 0 do > if a[j] = i then x := 1; fi; od; j-1; end; seq(A(n), n=1..67);

Extensions

Edited by Ray Chandler, Sep 01 2004