A078594 Number of pairs (x,y) 1<=x<=y<=n such that 1/x+1/y+1/n > 1/2.

1, 3, 6, 10, 15, 20, 24, 26, 29, 30, 33, 34, 36, 37, 38, 40, 42, 43, 45, 46, 48, 50, 52, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132

Offset

1,2

Links

Table of n, a(n) for n=1..64.

Formula

For n>=43, a(n) = 2*n+4 [Corrected by Sean A. Irvine, Jul 05 2025].

Prog

(PARI) a(n)=sum(i=1, n, sum(j=1, i, if(sign(1/i+1/j+1/n-1/2)-1, 0, 1)))

Crossrefs

Sequence in context: A080518 A310076 A307285 * A310077 A310078 A310079

Adjacent sequences: A078591 A078592 A078593 * A078595 A078596 A078597

Keyword

nonn

Author

Benoit Cloitre, Dec 08 2002

Status

approved