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 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. 7
 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 (list; graph; refs; listen; history; text; internal format)
 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: A109582 A308506 A255162 * A158045 A157304 A157305 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

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Last modified October 22 12:19 EDT 2021. Contains 348168 sequences. (Running on oeis4.)