cp's OEIS Frontend

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.

%I A333995 #42 Oct 14 2023 11:36:10
%S A333995 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 A333995 28,12,30,15,18,18,20,13,36,20,21,16,40,17,42,20,21,24,46,17,31,22,27,
%U A333995 23,52
%N 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.
%F A333995 a(n) = n - A108407(n-1) - A010051(n), n > 1. - Corrected by _R. J. Mathar_, Oct 02 2020
%F A333995 a(n) = A062854(n) - A010051(n) for n > 1. - _Chai Wah Wu_, Oct 14 2023
%e A333995 a(2) = 1 since the 1 X 1 and 2 X 2 multiplication tables are
%e A333995 ---
%e A333995   1
%e A333995 ---
%e A333995   1 2
%e A333995   2 4
%e A333995 ---
%e A333995 and the composite number 4 has appeared.
%e A333995 ---
%e A333995 a(8)=5:
%e A333995 .1..2..3..4..5..6..7....8
%e A333995 ....4..6..8.10.12.14...16
%e A333995 .......9.12.15.18.21...24
%e A333995 .........16.20.24.28...32 *
%e A333995 ............25.30.35...40 *
%e A333995 ...............36.42...48 *
%e A333995 ..................49...56 *
%e A333995 .......................64 *
%o A333995 (Python)
%o A333995 from itertools import takewhile
%o A333995 from sympy import divisors, isprime
%o A333995 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 A333995 Cf. A010051, A062854, A108407.
%K A333995 nonn
%O A333995 1,3
%A A333995 _Charles Kusniec_, Sep 05 2020