

A062854


First differences of A027424.


10



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
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OFFSET

1,2


COMMENTS

For prime p, a(p) = p.  Ralf Stephan, Jun 02 2005
a(n) is the number of times n appears in A033677.  Franklin T. AdamsWatters, Nov 18 2005
Conjecture: a(n) > n/log(n) for n > 2.  Thomas Ordowski, Jan 28 2017


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000


EXAMPLE

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).


MATHEMATICA

Prepend[Differences@ #, First@ #] &@ Module[{ u = {}}, Table[Length[u = Union[u, n Range@ n]], {n, 100}]] (* Michael De Vlieger, Jan 30 2017 *)


PROG

(PARI) b(n) = #setbinop((x, y)>x*y, vector(n, i, i); );
a(n) = b(n)  b(n1); \\ Michel Marcus, Jan 28 2017


CROSSREFS

Cf. A027421, A062854, A062855, A062856, A062857, A062859.
Sequence in context: A119674 A064920 A064916 * A057859 A242992 A029579
Adjacent sequences: A062851 A062852 A062853 * A062855 A062856 A062857


KEYWORD

nonn


AUTHOR

Ron Lalonde (ronronronlalonde(AT)hotmail.com), Jun 25 2001


EXTENSIONS

More terms from Ralf Stephan, Jun 02 2005


STATUS

approved



