A102354 a(n) is the number of ways n can be written as k^2 * j, 0 < j <= k.

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, 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, 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

Offset

1,64

Comments

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

Links

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

Formula

a(n) >= A102448(n). - Antti Karttunen, Aug 27 2017

Example

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

Mathematica

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

Prog

(PARI) A102354(n) = sumdiv(n, d, (issquare(d) && (sqrtint(d) >= (n/d)))); \\ Antti Karttunen, Aug 27 2017

Crossrefs

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

Sequence in context: A014082 A322583 A351439 * A370222 A349615 A157228

Adjacent sequences: A102351 A102352 A102353 * A102355 A102356 A102357

Keyword

nonn

Author

Leroy Quet, Feb 21 2005

Extensions

More terms from Robert G. Wilson v, Feb 22 2005

Status

approved