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A004434
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Numbers that are the sum of 5 distinct nonzero squares.
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9
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55, 66, 75, 79, 82, 87, 88, 90, 94, 95, 99, 100, 103, 106, 110, 111, 114, 115, 118, 120, 121, 123, 126, 127, 129, 130, 131, 132, 134, 135, 138, 139, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 154, 155, 156, 157, 158, 159, 160, 162, 163
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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Paul T. Bateman, Adolf J. Hildebrand, and George B. Purdy, Sums of distinct squares, Acta Arithmetica 67 (1994), pp. 349-380.
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FORMULA
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PROG
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(PARI) upto(lim)=my(v=List(), tb, tc, td, te); for(a=5, sqrt(lim), for(b=4, min(a-1, sqrt(lim-a^2)), tb=a^2+b^2; for(c=3, min(b-1, sqrt(lim-tb)), tc=tb+c^2; for(d=2, min(c-1, sqrt(lim-tc)), td=tc+d^2; for(e=1, d-1, te=td+e^2; if(te>lim, break, listput(v, te))))))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Jul 17 2011
(Haskell)
a004434 n = a004434_list !! (n-1)
a004434_list = filter (p 5 $ tail a000290_list) [1..] where
p k (q:qs) m = k == 0 && m == 0 ||
q <= m && k >= 0 && (p (k - 1) qs (m - q) || p k qs m)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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