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
Keywords
Examples
a(18) = 1 because 18 = k^2 * j, j <= k, gcd(k,j)=1, in one way: k=3, j=2.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..65537
Programs
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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 *) -
PARI
A102448(n) = sumdiv(n,d,((1==gcd(d,(n/d))) && issquare(d) && (sqrtint(d) >= (n/d)))); \\ Antti Karttunen, Aug 27 2017
Formula
a(n) <= A102354(n). - Antti Karttunen, Aug 27 2017
Extensions
More terms from Robert G. Wilson v, Feb 24 2005
Comments