A037092 Number of triples {i,j,k}, i>1, j>1, k>1, such that i*j*k < n^3.

0, 7, 35, 104, 238, 482, 851, 1402, 2147, 3179, 4497, 6210, 8324, 10921, 14048, 17759, 22146, 27247, 33158, 39953, 47652, 56372, 66135, 77187, 89351, 102902, 117801, 134252, 152148, 171853, 193328, 216471, 241557, 268780, 298017, 329515

Offset: 2

Author

Joe K. Crump (joecr(AT)carolina.rr.com)

Keywords

• nonn

Examples

			a(3) = 7 because the only triples i*j*k < 27 are (2,2,2) (2,2,3) (2,2,4) (2,2,5) (2,2,6) (2,3,3) (2,3,4).
		

Crossrefs

Cf. A037048.

Programs

PARI

a(n) = sum(i = 2, n-1, sum(j = i, sqrtint((n^3-1)/i), floor((n^3-1)/(i*j))-j+1)); \\ Michel Marcus, Sep 02 2013

Formula

a(n) = Sum_{i=2..n-1} Sum_{j=i..floor(sqrt((n^3-1)/i))} (floor((n^3-1)/(i*j))-j+1).