A104124 a(n) = number of ways to write n = (2m-1)^2 * k, m >= k, k and m = positive integers.

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

Offset

1,2601

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

Sum_{n>=1} a(n)/n = zeta(3)*7/4 + (1 - log(2))*Pi^2/4 - log(4).

a(n) >= A098108(n). - Antti Karttunen, Aug 27 2017

Example

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.

Prog

(PARI) A104124(n) = sumdiv(n, d, ((d%2) && issquare(d) && (((sqrtint(d)+1)/2) >= (n/d)))); \\ Antti Karttunen, Aug 27 2017

Crossrefs

Cf. A098108.

Sequence in context: A359160 A373978 A326499 * A347246 A052434 A369034

Adjacent sequences: A104121 A104122 A104123 * A104125 A104126 A104127

Keyword

nonn

Author

Leroy Quet, Mar 06 2005

Extensions

More terms from R. J. Mathar, Feb 14 2008

Status

approved