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%I #42 Oct 14 2023 11:36:10
%S 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,
%T 28,12,30,15,18,18,20,13,36,20,21,16,40,17,42,20,21,24,46,17,31,22,27,
%U 23,52
%N 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.
%F a(n) = n - A108407(n-1) - A010051(n), n > 1. - Corrected by _R. J. Mathar_, Oct 02 2020
%F a(n) = A062854(n) - A010051(n) for n > 1. - _Chai Wah Wu_, Oct 14 2023
%e a(2) = 1 since the 1 X 1 and 2 X 2 multiplication tables are
%e ---
%e 1
%e ---
%e 1 2
%e 2 4
%e ---
%e and the composite number 4 has appeared.
%e ---
%e a(8)=5:
%e .1..2..3..4..5..6..7....8
%e ....4..6..8.10.12.14...16
%e .......9.12.15.18.21...24
%e .........16.20.24.28...32 *
%e ............25.30.35...40 *
%e ...............36.42...48 *
%e ..................49...56 *
%e .......................64 *
%o (Python)
%o from itertools import takewhile
%o from sympy import divisors, isprime
%o 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
%Y Cf. A010051, A062854, A108407.
%K nonn
%O 1,3
%A _Charles Kusniec_, Sep 05 2020
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