login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A362932
a(n) = A132188(n) - A362931(n).
3
0, 0, 0, 2, 2, -2, -2, 0, 4, 4, 4, 2, 2, 2, -2, 4, 4, 4, 4, 2, 2, 2, 2, 0, 8, 8, 12, 10, 10, 2, 2, 8, 8, 8, 4, 10, 10, 10, 10, 8, 8, 0, 0, 2, -2, -2, -2, 0, 12, 20, 20, 22, 22, 22, 22, 20, 20, 20, 20, 10, 10, 10, 10, 24, 24, 16, 16, 18, 18, 14, 14, 16, 16, 16, 20, 22, 18, 14, 14, 16
OFFSET
1,4
COMMENTS
a(n) = (number of pairs (i,j) in [1..n] X [1..n] with integral geometric mean sqrt(i*j)) - (number of pairs (i,j) in [1..n] X [1..n] with integral harmonic mean 2*i*j/(i+j)).
LINKS
MAPLE
a:= proc(n) option remember; `if`(n=0, 0, 2*add(
`if`(irem(2*i*n, i+n)=0, -1, 0)+
`if`(issqr(i*n), 1, 0), i=1..n-1)+a(n-1))
end:
seq(a(n), n=1..80); # Alois P. Heinz, Aug 28 2023
MATHEMATICA
Block[{c, q}, c[n_] := c[n] = Flatten[Table[w^2 - x*y, {w, n}, {x, n}, {y, n}]]; q[n_] := q[n] = Flatten[Table[(2*i*j)/(i + j), {i, n}, {j, n}]]; Table[Count[c[n], 0] - Count[q[n], _?IntegerQ], {n, 80}] ] (* Michael De Vlieger, Aug 28 2023 *)
PROG
(Python)
from sympy.ntheory.primetest import is_square
def A362932(n): return sum((1 if T else -1) for x in range(1, n+1) for y in range(1, x) if (T:=is_square(x*y))^(not (x*y<<1)%(x+y)))<<1 # Chai Wah Wu, Aug 28 2023
CROSSREFS
Sequence in context: A268243 A159782 A268242 * A309509 A216953 A326786
KEYWORD
sign,look
AUTHOR
N. J. A. Sloane, Aug 28 2023
STATUS
approved