A062851 Number of k such that 1 < k < n X n and k not of the form ij for 1 <= {i, j} <= n.

0, 1, 3, 7, 11, 18, 24, 34, 45, 58, 68, 85, 97, 116, 136, 159, 175, 201, 219, 248, 277, 308, 330, 367, 400, 437, 475, 517, 545, 592, 622, 670, 717, 766, 815, 873, 909, 964, 1020, 1083, 1123, 1189, 1231, 1298, 1366, 1433, 1479, 1557, 1623, 1700, 1774, 1854

Offset

1,3

Comments

Smallest k for given n is given by A007918, largest by A005563 (except for some initial terms).

Links

Table of n, a(n) for n=1..52.

Example

a(4)=7 because there are 9 unique products in the 4 X 4 multiplication table (1 2 3 4 6 8 9 12 16), which excludes 7 non-product integers within the range 1 to 16 (5 7 10 11 13 14 15).

Prog

(Python)
def A062851(n): return n**2-len({i*j for i in range(1, n+1) for j in range(1, i+1)}) # Chai Wah Wu, Oct 13 2023

Crossrefs

a(n) = n^2 - A027424.

Cf. A027424, A062854, A062855, A062856, A062857, A062859.

Sequence in context: A190711 A210977 A049792 * A178464 A071979 A335323

Adjacent sequences: A062848 A062849 A062850 * A062852 A062853 A062854

Keyword

nonn

Author

Ron A. Lalonde (ronronronlalonde(AT)hotmail.com), Jun 25 2001

Status

approved