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A104124
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a(n) = number of ways to write n = (2m-1)^2 * k, m >= k, k and m = positive integers.
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1
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1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1,2601
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COMMENTS
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The first entries > 1 are a(2601) = a(3249) = a(3969) = a(4761) = a(5625) = 2. - R. J. Mathar, Feb 14 2008
The first entries > 2 are a(65025) = a(81225) = a(99225) = 3. - R. J. Mathar, Feb 14 2008
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LINKS
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FORMULA
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Sum_{n>=1} a(n)/n = zeta(3)*7/4 + (1 - log(2))*Pi^2/4 - log(4).
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EXAMPLE
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1 = (2*1-1)^2*1.
9 = (2*2-1)^2*1.
18 = (2*2-1)^2*2.
25 = (2*3-1)^2*1.
49 = (2*4-1)^2*1.
50 = (2*3-1)^2*2.
75 = (2*3-1)^2*3.
81 = (2*5-1)^2*1.
98 = (2*4-1)^2*2.
121 = (2*6-1)^2*1.
147 = (2*4-1)^2*3.
162 = (2*5-1)^2*2.
169 = (2*7-1)^2*1.
196 = (2*4-1)^2*4.
225 = (2*8-1)^2*1.
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PROG
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(PARI) A104124(n) = sumdiv(n, d, ((d%2) && issquare(d) && (((sqrtint(d)+1)/2) >= (n/d)))); \\ Antti Karttunen, Aug 27 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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