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

1,2

Comments

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

Links

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.

Example

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

Maple

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

Crossrefs

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

Sequence in context: A367588 A320033 A333527 * A335152 A111899 A074753

Adjacent sequences: A064044 A064045 A064046 * A064048 A064049 A064050

Keyword

nonn

Author

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

Status

approved