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A062854
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First differences of A027424.
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11
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1, 2, 3, 3, 5, 4, 7, 5, 6, 6, 11, 6, 13, 8, 9, 8, 17, 9, 19, 10, 12, 12, 23, 10, 16, 14, 15, 13, 29, 12, 31, 15, 18, 18, 20, 13, 37, 20, 21, 16, 41, 17, 43, 20, 21, 24, 47, 17, 31, 22, 27, 23, 53, 22, 31, 22, 30, 30, 59, 19, 61, 32, 28, 26, 36, 26, 67, 30, 36, 26, 71, 23, 73, 38
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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For prime p, a(p) = p. - Ralf Stephan, Jun 02 2005
a(n) is the number of times n appears in A033677. - Franklin T. Adams-Watters, Nov 18 2005
Conjecture: a(n) > n/log(n) for n > 2. - Thomas Ordowski, Jan 28 2017
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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EXAMPLE
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a(4)=3 because there are 9 unique products in the 4 X 4 multiplication table (1 2 3 4 6 8 9 12 16), which is 3 more than the 6 unique products in the 3 X 3 multiplication table (1 2 3 4 6 9).
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MAPLE
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A062854 := proc(n)
A027424(n)-A027424(n-1) ;
end proc:
seq(A062854(n), n=1..40) ; # R. J. Mathar, Oct 02 2020
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MATHEMATICA
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Prepend[Differences@ #, First@ #] &@ Module[{ u = {}}, Table[Length[u = Union[u, n Range@ n]], {n, 100}]] (* Michael De Vlieger, Jan 30 2017 *)
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PROG
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(PARI) b(n) = #setbinop((x, y)->x*y, vector(n, i, i); );
a(n) = b(n) - b(n-1); \\ Michel Marcus, Jan 28 2017
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CROSSREFS
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Cf. A027421, A062854, A062855, A062856, A062857, A062859.
Sequence in context: A119674 A064920 A064916 * A057859 A242992 A029579
Adjacent sequences: A062851 A062852 A062853 * A062855 A062856 A062857
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KEYWORD
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nonn
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AUTHOR
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Ron Lalonde (ronronronlalonde(AT)hotmail.com), Jun 25 2001
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EXTENSIONS
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More terms from Ralf Stephan, Jun 02 2005
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STATUS
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approved
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