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a(n) is the number of ways n can be written as k^2 * j, 0 < j <= k.
8

%I #20 Aug 27 2017 12:55:14

%S 1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,

%T 0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,

%U 0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,0,0,0,0

%N a(n) is the number of ways n can be written as k^2 * j, 0 < j <= k.

%C Sum_{n>0} a(n)/n = 2*zeta(3). See A152648.

%H Antti Karttunen, <a href="/A102354/b102354.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) >= A102448(n). - _Antti Karttunen_, Aug 27 2017

%e a(18) = 1 because 18 = k^2 * j, j <= k, in one way: k=3, j=2.

%t t = Sort[ Flatten[ Table[k^2*j, {k, 11}, {j, k}]]]; Table[ Count[t, n], {n, 105}] (* _Robert G. Wilson v_, Feb 22 2005 *)

%o (PARI) A102354(n) = sumdiv(n,d,(issquare(d) && (sqrtint(d) >= (n/d)))); \\ _Antti Karttunen_, Aug 27 2017

%Y Cf. A102448, A104020, A104022, A104024, A152648.

%K nonn

%O 1,64

%A _Leroy Quet_, Feb 21 2005

%E More terms from _Robert G. Wilson v_, Feb 22 2005