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A064047 Number of numbers only appearing once in 1-to-n multiplication table. 4
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A367588 A320033 A333527 * A335152 A111899 A074753
KEYWORD
nonn
AUTHOR
Matthew Somerville (matthew.somerville(AT)trinity.oxford.ac.uk), Aug 24 2001
STATUS
approved

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Last modified February 21 12:17 EST 2024. Contains 370235 sequences. (Running on oeis4.)