A333995 a(n) = number of distinct composite numbers in the n X n multiplication table that are not in the n-1 X n-1 multiplication table.

0, 1, 2, 3, 4, 4, 6, 5, 6, 6, 10, 6, 12, 8, 9, 8, 16, 9, 18, 10, 12, 12, 22, 10, 16, 14, 15, 13, 28, 12, 30, 15, 18, 18, 20, 13, 36, 20, 21, 16, 40, 17, 42, 20, 21, 24, 46, 17, 31, 22, 27, 23, 52

Offset: 1

Author

Charles Kusniec, Sep 05 2020

Keywords

• nonn

Examples

			a(2) = 1 since the 1 X 1 and 2 X 2 multiplication tables are
---
  1
---
  1 2
  2 4
---
and the composite number 4 has appeared.
---
a(8)=5:
.1..2..3..4..5..6..7....8
....4..6..8.10.12.14...16
.......9.12.15.18.21...24
.........16.20.24.28...32 *
............25.30.35...40 *
...............36.42...48 *
..................49...56 *
.......................64 *
		

Crossrefs

Cf. A010051, A062854, A108407.

Programs

Python

from itertools import takewhile
from sympy import divisors, isprime
def A333995(n): return sum(1 for i in range(1,n+1) if all(d<=i for d in takewhile(lambda d:d1 else 0 # Chai Wah Wu, Oct 14 2023

Formula

a(n) = n - A108407(n-1) - A010051(n), n > 1. - Corrected by R. J. Mathar, Oct 02 2020

a(n) = A062854(n) - A010051(n) for n > 1. - Chai Wah Wu, Oct 14 2023