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 A062854 First differences of A027424. 10

%I

%S 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,

%T 29,12,31,15,18,18,20,13,37,20,21,16,41,17,43,20,21,24,47,17,31,22,27,

%U 23,53,22,31,22,30,30,59,19,61,32,28,26,36,26,67,30,36,26,71,23,73,38

%N First differences of A027424.

%C For prime p, a(p) = p. - _Ralf Stephan_, Jun 02 2005

%C a(n) is the number of times n appears in A033677. - _Franklin T. Adams-Watters_, Nov 18 2005

%C Conjecture: a(n) > n/log(n) for n > 2. - _Thomas Ordowski_, Jan 28 2017

%H T. D. Noe, <a href="/A062854/b062854.txt">Table of n, a(n) for n=1..1000</a>

%e 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).

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

%o (PARI) b(n) = #setbinop((x, y)->x*y, vector(n, i, i); );

%o a(n) = b(n) - b(n-1); \\ _Michel Marcus_, Jan 28 2017

%Y Cf. A027421, A062854, A062855, A062856, A062857, A062859.

%K nonn

%O 1,2

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

%E More terms from _Ralf Stephan_, Jun 02 2005

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)