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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.
4
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
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
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1
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1 2
2 4
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and the composite number 4 has appeared.
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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
KEYWORD
nonn
AUTHOR
Charles Kusniec, Sep 05 2020
STATUS
approved