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

1,3

Links

Table of n, a(n) for n=1..53.

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

Example

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 *

Prog

(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:d<n, divisors(n*i))))-int(isprime(n)) if n>1 else 0 # Chai Wah Wu, Oct 14 2023

Crossrefs

Cf. A010051, A062854, A108407.

Sequence in context: A298933 A365851 A091860 * A301764 A181833 A202650

Adjacent sequences: A333992 A333993 A333994 * A333996 A333997 A333998

Keyword

nonn

Author

Charles Kusniec, Sep 05 2020

Status

approved