A362935 a(n) = (A000982(n) - A132188(n))/2.

0, 0, 1, 1, 3, 5, 8, 10, 12, 16, 21, 25, 31, 37, 44, 48, 56, 62, 71, 79, 89, 99, 110, 120, 128, 140, 151, 163, 177, 191, 206, 218, 234, 250, 267, 279, 297, 315, 334, 352, 372, 392, 413, 433, 453, 475, 498, 518, 536, 556, 581, 605, 631, 655, 682, 708, 736, 764, 793, 821, 851, 881, 910, 934, 966, 998

Offset

1,5

Comments

a(n) = one-half of (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

Formula

a(n) = A362934(n)/2.

Prog

(Python)
from sympy.ntheory.primetest import is_square
def A362935(n): return ((n-1)**2>>2)-sum(1 for x in range(1, n+1) for y in range(1, x) if is_square(x*y)) # Chai Wah Wu, Aug 29 2023

Crossrefs

Cf. A000982, A132188, A362931-A932937.

Sequence in context: A079527 A287236 A305378 * A033033 A211704 A275813

Adjacent sequences: A362932 A362933 A362934 * A362936 A362937 A362938

Keyword

nonn

Author

N. J. A. Sloane, Aug 28 2023

Status

approved