A362931 - OEIS

%I #20 Aug 29 2023 11:15:08

%S 1,2,3,4,5,10,11,12,13,14,15,20,21,22,27,28,29,34,35,40,41,42,43,48,

%T 49,50,51,56,57,66,67,68,69,70,75,80,81,82,83,88,89,98,99,100,109,110,

%U 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

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

%H Alois P. Heinz, <a href="/A362931/b362931.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n + Sum_{1<=i<j<=n, (i+j)|2*i*j} 2. - _Chai Wah Wu_, Aug 28 2023

%p a:= proc(n) option remember; `if`(n=0, 0, a(n-1)-1+

%p       2*add(`if`(irem(2*i*n, i+n)=0, 1, 0), i=1..n))

%p     end:

%p seq(a(n), n=1..80);  # _Alois P. Heinz_, Aug 28 2023

%o (Python)

%o 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

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

%Y Cf. also A362932-A362937.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Aug 28 2023