A104124 - OEIS

%I #25 Jan 10 2023 01:21:03

%S 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,

%T 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,

%U 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

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

%C The first entries > 1 are a(2601) = a(3249) = a(3969) = a(4761) = a(5625) = 2. - _R. J. Mathar_, Feb 14 2008

%C The first entries > 2 are a(65025) = a(81225) = a(99225) = 3. - _R. J. Mathar_, Feb 14 2008

%H Antti Karttunen, <a href="/A104124/b104124.txt">Table of n, a(n) for n = 1..65537</a>

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

%F a(n) >= A098108(n). - _Antti Karttunen_, Aug 27 2017

%e 1 = (2*1-1)^2*1.

%e 9 = (2*2-1)^2*1.

%e 18 = (2*2-1)^2*2.

%e 25 = (2*3-1)^2*1.

%e 49 = (2*4-1)^2*1.

%e 50 = (2*3-1)^2*2.

%e 75 = (2*3-1)^2*3.

%e 81 = (2*5-1)^2*1.

%e 98 = (2*4-1)^2*2.

%e 121 = (2*6-1)^2*1.

%e 147 = (2*4-1)^2*3.

%e 162 = (2*5-1)^2*2.

%e 169 = (2*7-1)^2*1.

%e 196 = (2*4-1)^2*4.

%e 225 = (2*8-1)^2*1.

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

%Y Cf. A098108.

%K nonn

%O 1,2601

%A _Leroy Quet_, Mar 06 2005

%E More terms from _R. J. Mathar_, Feb 14 2008