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A100073
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Number of representations of n as the difference of two positive squares.
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0
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0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 2, 1, 1, 0, 1, 1, 2, 0, 1, 2, 1, 0, 2, 1, 1, 0, 1, 2, 2, 0, 2, 1, 1, 0, 2, 2, 1, 0, 1, 1, 3, 0, 1, 3, 1, 0, 2, 1, 1, 0, 2, 2, 2, 0, 1, 2, 1, 0, 3, 2, 2, 0, 1, 1, 2, 0, 1, 3, 1, 0, 3, 1, 2, 0, 1, 3, 2, 0, 1, 2, 2, 0, 2, 2, 1, 0, 2, 1, 2, 0, 2, 4, 1, 0, 3, 1, 1, 0, 1, 2, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,15
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COMMENTS
| Note that for odd n, a(n) = 1 iff n is a prime, or a prime squared.
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FORMULA
| a(n) = A056924(n) for odd n, a(n) = A056924(n/4) if 4|n, otherwise a(n) = 0.
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EXAMPLE
| a(15) = 2 because 15 = 16-1 = 64-49.
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MATHEMATICA
| nn=150; a=Table[0, {nn}]; Do[y=x-1; While[d=x^2-y^2; d<=nn&&y>0, a[[d]]++; y-- ], {x, 1+nn/2}]; a
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CROSSREFS
| Cf. A056924 (number of divisors of n that are less than sqrt(n)), A016825 (numbers not the difference of two squares), A034178 (number of representations of n as the difference of two squares).
Sequence in context: A026920 A060763 A131576 * A075685 A037906 A120936
Adjacent sequences: A100070 A100071 A100072 * A100074 A100075 A100076
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KEYWORD
| easy,nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Nov 02 2004
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