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A362931
a(n) = number of pairs (i,j) in [1..n] X [1..n] with integral harmonic mean 2*i*j/(i+j).
9
1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, 27, 28, 29, 34, 35, 40, 41, 42, 43, 48, 49, 50, 51, 56, 57, 66, 67, 68, 69, 70, 75, 80, 81, 82, 83, 88, 89, 98, 99, 100, 109, 110, 111, 116, 117, 118, 119, 120, 121, 126, 127, 132, 133, 134, 135, 148, 149, 150, 155, 156, 157, 166, 167, 168, 169, 174, 175, 184, 185, 186, 191, 192, 197, 202, 203, 208
OFFSET
1,2
LINKS
FORMULA
a(n) = n + Sum_{1<=i<j<=n, (i+j)|2*i*j} 2. - Chai Wah Wu, Aug 28 2023
MAPLE
a:= proc(n) option remember; `if`(n=0, 0, a(n-1)-1+
2*add(`if`(irem(2*i*n, i+n)=0, 1, 0), i=1..n))
end:
seq(a(n), n=1..80); # Alois P. Heinz, Aug 28 2023
MATHEMATICA
a[n_] := a[n] = If[n == 0, 0, a[n-1] - 1 +
2*Sum[If[Mod[2*i*n, i+n] == 0, 1, 0], {i, 1, n}]];
Table[a[n], {n, 1, 80}] (* Jean-François Alcover, Oct 13 2024, after Alois P. Heinz *)
PROG
(Python)
def A362931(n): return n+(sum(1 for x in range(1, n+1) for y in range(1, x) if not (x*y<<1)%(x+y))<<1) # Chai Wah Wu, Aug 28 2023
CROSSREFS
Cf. A000982 (arithmetic mean analog), A132188 (geometric mean analog).
Cf. also A362932-A362937.
Sequence in context: A037473 A007092 A241213 * A375514 A047596 A199502
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 28 2023
STATUS
approved