A362934 a(n) = A000982(n) - A132188(n).

0, 0, 2, 2, 6, 10, 16, 20, 24, 32, 42, 50, 62, 74, 88, 96, 112, 124, 142, 158, 178, 198, 220, 240, 256, 280, 302, 326, 354, 382, 412, 436, 468, 500, 534, 558, 594, 630, 668, 704, 744, 784, 826, 866, 906, 950, 996, 1036, 1072, 1112, 1162, 1210, 1262, 1310, 1364, 1416, 1472, 1528, 1586, 1642, 1702, 1762

Offset: 1

Author

N. J. A. Sloane, Aug 28 2023

Keywords

• nonn

Comments

a(n) = (number of pairs (i,j) in [1..n] X [1..n] with integral arithmetic mean) - (number of pairs (i,j) in [1..n] X [1..n] with integral geometric mean).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000982, A132188, A362931-A932937.

Programs

Python

from sympy.ntheory.primetest import is_square
def A362934(n): return ((n-1)**2>>1)-(sum(1 for x in range(1,n+1) for y in range(1,x) if is_square(x*y))<<1) # Chai Wah Wu, Aug 29 2023