A331532 a(n) is the number of nonnegative integers k such that (n^2) AND (k^2) = k^2 (where AND denotes the bitwise AND operator).
1, 2, 2, 3, 2, 5, 3, 4, 2, 5, 5, 9, 3, 4, 4, 4, 2, 4, 5, 7, 5, 12, 9, 4, 3, 9, 4, 11, 4, 7, 4, 6, 2, 5, 4, 7, 5, 12, 7, 15, 5, 7, 12, 13, 9, 17, 4, 3, 3, 7, 9, 4, 4, 20, 11, 15, 4, 8, 7, 12, 4, 5, 6, 6, 2, 4, 5, 7, 4, 11, 7, 14, 5, 12, 12, 29, 7, 8, 15, 5, 5
Offset: 0
Examples
For n = 7: - we have: k 7^2 AND k^2 - ----------- 0 0 = 0 1 1 = 1 2 0 <> 4 3 1 <> 9 4 16 = 16 5 17 <> 25 6 32 <> 36 7 49 = 49 - hence a(7) = 4.
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..8192
- Rémy Sigrist, Scatterplot of (x, y) such that (x^2) AND (y^2) = y^2, with 0 <= x <= 1024
Programs
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PARI
a(n) = sum(k=0, n, bitand(n^2, k^2)==k^2)
Formula
a(2^k) = 2 for any k >= 0.
a(n) <= n+1.
Comments