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A064047 Number of numbers only appearing once in 1-to-n multiplication table.

%I A064047 #20 Mar 29 2022 17:08:03
%S A064047 1,2,3,3,4,5,6,6,5,6,7,8,9,10,11,10,11,12,13,13,14,15,16,17,15,16,15,
%T A064047 15,16,17,18,17,18,19,20,20,21,22,23,24,25,26,27,27,28,29,30,30,26,26,
%U A064047 27,27,28,29,30,31,32,33,34,35,36,37,38,36,37,38,39,39,40,41,42,42,43
%N A064047 Number of numbers only appearing once in 1-to-n multiplication table.
%C A064047 For n <= 127, this is the same as the number of vertices of the polytope representing the number n. The latter is given in A335152. The sequences differ starting at n = 128. See A335152 and Lu and Deng, Appendix. - _N. J. A. Sloane_, May 25 2020
%C A064047 a(n) is the number of x in [1,n] such that x^2 has no divisor d with x < d <= n. - _Robert Israel_, Sep 03 2020
%H A064047 Robert Israel, <a href="/A064047/b064047.txt">Table of n, a(n) for n = 1..10000</a>
%H A064047 Ya-Ping Lu and Shu-Fang Deng, <a href="http://arxiv.org/abs/2003.08968">Properties of Polytopes Representing Natural Numbers</a>, arXiv:2003.08968 [math.GM], 2020.
%e A064047 In the 1-to-5 multiplication table, four numbers (1,9,16,25) appear once only. Therefore a(5)=4.
%p A064047 N:= 200: # for a(1)..a(N)
%p A064047 V:= Vector(N):
%p A064047 for x from 1 to N do
%p A064047   y:= min(N, min(select(`>`,numtheory:-divisors(x^2),x))-1);
%p A064047   V[x..y]:= map(`+`,V[x..y],1)
%p A064047 od:
%p A064047 convert(V,list); # _Robert Israel_, Sep 03 2020
%Y A064047 Cf. A064048, A057142, A057143, A057144, A335152.
%K A064047 nonn
%O A064047 1,2
%A A064047 Matthew Somerville (matthew.somerville(AT)trinity.oxford.ac.uk), Aug 24 2001