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

0,1

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

Links

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

Example

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.

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);

Crossrefs

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

Sequence in context: A308506 A255162 A359006 * A360643 A158045 A157304

Adjacent sequences: A097560 A097561 A097562 * A097564 A097565 A097566

Keyword

easy,sign

Author

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

Extensions

Edited by Ray Chandler, Sep 01 2004

Status

approved