

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).


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Equivalently, this is the number of nonnegative integers k such that (n^2) OR (k^2) = n^2 (where OR denotes the bitwise OR operator); this connects this sequence to A001316.


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


FORMULA

a(2^k) = 2 for any k >= 0.
a(n) <= n+1.


EXAMPLE

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.


PROG

(PARI) a(n) = sum(k=0, n, bitand(n^2, k^2)==k^2)


CROSSREFS

Cf. A001316, A331533 (corresponding k's).
Sequence in context: A025478 A084371 A025476 * A078773 A151663 A162753
Adjacent sequences: A331529 A331530 A331531 * A331533 A331534 A331535


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Jan 19 2020


STATUS

approved



