A362931 a(n) = number of pairs (i,j) in [1..n] X [1..n] with integral harmonic mean 2*i*j/(i+j).

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

Author

N. J. A. Sloane, Aug 28 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A000982 (arithmetic mean analog), A132188 (geometric mean analog).

Cf. also A362932-A362937.

Programs

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 *)

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

Formula

a(n) = n + Sum_{1<=iChai Wah Wu, Aug 28 2023