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A108407 Number of added unique known entries when going from the n X n to the (n+1) X (n+1) multiplication table. 6
0, 0, 1, 0, 2, 0, 3, 3, 4, 0, 6, 0, 6, 6, 8, 0, 9, 0, 10, 9, 10, 0, 14, 9, 12, 12, 15, 0, 18, 0, 17, 15, 16, 15, 23, 0, 18, 18, 24, 0, 25, 0, 24, 24, 22, 0, 31, 18, 28, 24, 29, 0, 32, 24, 34, 27, 28, 0, 41, 0, 30, 35, 38, 29, 40, 0, 38, 33, 44, 0, 49, 0, 36, 41, 43, 32, 47, 0, 52 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..1000

FORMULA

For prime p, a(p-1) = 0.

a(n) = n+1 - A062854(n+1).

EXAMPLE

When going to 8 X 8, the added entries 8,16,24 are already known, so a(7)=3:

.1..2..3..4..5..6..7....8 *

....4..6..8.10.12.14...16 *

.......9.12.15.18.21...24 *

.........16.20.24.28...32

............25.30.35...40

...............36.42...48

..................49...56

.......................64

MAPLE

A108407 := proc(n)

    n+1-A062854(n+1) ;

end proc:

seq(A108407(n), n=1..40) ; # R. J. Mathar, Oct 02 2020

MATHEMATICA

nmax = 100;

A062854 = Table[u = If[n == 1, {}, Union[u, n Range[n]]]; Length[u], {n, 1, nmax+1}] // Differences // Prepend[#, 1]&;

a[n_] := n + 1 - A062854[[n+1]];

Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Oct 02 2020 *)

CROSSREFS

Unique values of sequence are in A108408.

Cf. A027424 (total unique entries), A062854 (added unique unknown entries).

Sequence in context: A291307 A239313 A046667 * A180772 A291304 A245332

Adjacent sequences:  A108404 A108405 A108406 * A108408 A108409 A108410

KEYWORD

nonn

AUTHOR

Ralf Stephan, Jun 03 2005

STATUS

approved

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Last modified December 2 05:01 EST 2021. Contains 349437 sequences. (Running on oeis4.)