A102448 a(n) is the number of ways to write n = k^2 * j, j <= k, gcd(k,j) = 1, where j and k are positive integers.

1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 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, 1, 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, 2, 0, 0, 0, 0, 0

Offset

1,100

Comments

Sum_{n>0} a(n)/n = 2.

Links

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

Formula

a(n) <= A102354(n). - Antti Karttunen, Aug 27 2017

Example

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

Mathematica

t = Sort[ Flatten[ Table[ If[ GCD[j, k] == 1, k^2*j, {}], {k, 11}, {j, k}]]]; Table[ Count[t, n], {n, 105}] (* Robert G. Wilson v, Feb 25 2005 *)

Prog

(PARI) A102448(n) = sumdiv(n, d, ((1==gcd(d, (n/d))) && issquare(d) && (sqrtint(d) >= (n/d)))); \\ Antti Karttunen, Aug 27 2017

Crossrefs

Cf. A102354, A104021, A104023, A104025.

Sequence in context: A277149 A062892 A118553 * A102683 A122840 A083919

Adjacent sequences: A102445 A102446 A102447 * A102449 A102450 A102451

Keyword

nonn

Author

Leroy Quet, Feb 23 2005

Extensions

More terms from Robert G. Wilson v, Feb 24 2005

Status

approved