A064048 -id:A064048 - cp's OEIS frontend

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

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, 15, 16, 17, 18, 17, 18, 19, 20, 20, 21, 22, 23, 24, 25, 26, 27, 27, 28, 29, 30, 30, 26, 26, 27, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 36, 37, 38, 39, 39, 40, 41, 42, 42, 43

Offset: 1

Matthew Somerville (matthew.somerville(AT)trinity.oxford.ac.uk), Aug 24 2001

nonn

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

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

			In the 1-to-5 multiplication table, four numbers (1,9,16,25) appear once only. Therefore a(5)=4.

Robert Israel, Table of n, a(n) for n = 1..10000
Ya-Ping Lu and Shu-Fang Deng, Properties of Polytopes Representing Natural Numbers, arXiv:2003.08968 [math.GM], 2020.

Cf. A064048, A057142, A057143, A057144, A335152.

N:= 200: # for a(1)..a(N)
V:= Vector(N):
for x from 1 to N do
  y:= min(N, min(select(`>`,numtheory:-divisors(x^2),x))-1);
  V[x..y]:= map(`+`,V[x..y],1)
od:
convert(V,list); # Robert Israel, Sep 03 2020

cp's OEIS Frontend

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

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