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A094739
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Numbers n such that 4^k n, for k >= 0, are numbers having a unique partition into three squares.
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4
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1, 2, 3, 5, 6, 10, 11, 13, 14, 19, 21, 22, 30, 35, 37, 42, 43, 46, 58, 67, 70, 78, 91, 93, 115, 133, 142, 163, 190, 235, 253, 403, 427
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Lehmer's paper has an erroneous version of this sequence. He omits 163 and includes 162 (which has 4 partitions) and 182 (which has 3 partitions). Lemher conjectures that there are no more terms. Note that squares are allowed to be zero.
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REFERENCES
| D. H. Lehmer, On the partition of numbers into squares, Amer. Math. Monthly, Vol. 55, No. 8 (Oct 1948), 476-481.
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EXAMPLE
| 163 is in this sequence because 163 = 1+81+81 is the unique partition of 163.
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MATHEMATICA
| lim=100; nLst=Table[0, {lim^2}]; Do[n=a^2+b^2+c^2; If[n>0 && n<lim^2, nLst[[n]]++ ], {a, 0, lim}, {b, a, Sqrt[lim^2-a^2]}, {c, b, Sqrt[lim^2-a^2-b^2]}]; Select[Flatten[Position[nLst, 1]], Mod[ #, 4]>0&]
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CROSSREFS
| Cf. A005875 (number of ways of writing n as the sum of three squares), A094740 (n having a unique partition into three positive squares).
Sequence in context: A014593 A034044 A047447 * A063451 A178992 A076474
Adjacent sequences: A094736 A094737 A094738 * A094740 A094741 A094742
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), May 24 2004
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