A087062 -id:A087062 - cp's OEIS frontend

A004197 Triangle read by rows. T(n, k) = n - k if n - k < k, otherwise k.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2

Offset: 0

David W. Wilson

Table of min(x,y), where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),...
Highest power of 6 that divides A036561. - Fred Daniel Kline, May 29 2012
Triangle T(n,k) read by rows: T(n,k) = min(k,n-k). - Philippe Deléham, Feb 25 2014

			From _Philippe Deléham_, Feb 25 2014: (Start)
Top left corner of table:
  0 0 0 0
  0 1 1 1
  0 1 2 2
  0 1 2 3
Triangle T(n,k) begins:
  0;
  0, 0;
  0, 1, 0;
  0, 1, 1, 0;
  0, 1, 2, 1, 0;
  0, 1, 2, 2, 1, 0;
  0, 1, 2, 3, 2, 1, 0;
  0, 1, 2, 3, 3, 2, 1, 0;
  0, 1, 2, 3, 4, 3, 2, 1, 0;
  0, 1, 2, 3, 4, 4, 3, 2, 1, 0;
  0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0;
  0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0;
  0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0;
  0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0;
  0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 0;
  0, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 0;
  ... (End)

Reinhard Zumkeller, Rows n=0..100 of triangle, flattened

Similar to but strictly different from A087062 and A261684.
Row sums give A002620. - Reinhard Zumkeller, Jul 27 2005
Positions of zero are given in A117142. - Ridouane Oudra, Apr 30 2019
Cf. A144464, A152714, A152716, A152717.

a004197 n k = a004197_tabl !! n !! k
a004197_tabl = map a004197_row [0..]
a004197_row n = hs ++ drop (1 - n `mod` 2) (reverse hs)
   where hs = [0..n `div` 2]
-- Reinhard Zumkeller, Aug 14 2011

T := (n, k) -> if n - k < k then n - k else k fi:
for n from 0 to 9 do seq(T(n, k), k=0..n) od; # Peter Luschny, May 07 2023

Flatten[Table[IntegerExponent[2^(n - k) 3^k, 6], {n, 0, 20}, {k, 0, n}]] (* Fred Daniel Kline, May 29 2012 *)

T(x,y)=min(x,y) \\ Charles R Greathouse IV, Feb 07 2017

a(n) = A003983(n) - 1.
G.f.: x*y/((1-x)*(1-y)*(1-x*y)). - Franklin T. Adams-Watters, Feb 06 2006
2^T(n,k) = A144464(n,k), 3^T(n,k) = A152714(n,k), 4^T(n,k) = A152716(n,k), 5^T(n,k) = A152717(n,k). - Philippe Deléham, Feb 25 2014
a(n) = (1/2)*(t - 1 - abs(t^2 - 2*n - 1)), where t = floor(sqrt(2*n+1)+1/2). - Ridouane Oudra, May 03 2019

Mathematica program fixed by Harvey P. Dale, Nov 26 2020

Name edited by Peter Luschny, May 07 2023

A087029 Number of lunar divisors of n (unbounded version).

Original entry on oeis.org

9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 90, 16, 14, 12, 10, 8, 6, 4, 2, 16, 16, 72, 14, 12, 10, 8, 6, 4, 2, 14, 14, 14, 56, 12, 10, 8, 6, 4, 2, 12, 12, 12, 12, 42, 10, 8, 6, 4, 2, 10, 10, 10, 10, 10, 30, 8, 6, 4, 2, 8, 8, 8, 8, 8, 8, 20, 6, 4, 2, 6, 6, 6, 6, 6, 6, 6, 12, 4, 2, 4, 4, 4, 4

Offset: 1

Marc LeBrun and N. J. A. Sloane, Oct 19 2003

Number of d, 1 <= d < infinity, such that there exists an e, 1 <= e < infinity, with d*e = n, where * is lunar multiplication.

			The 18 divisors of 10 are 1, 2, ..., 9, 10, 20, 30, ..., 90, so a(10) = 18.

D. Applegate, Table of n, a(n) for n = 1..100000
D. Applegate, C program for lunar arithmetic and number theory
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arxiv:1107.1130 [math-NT], July 2011. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
Brady Haran and N. J. A. Sloane, Primes on the Moon (Lunar Arithmetic), Numberphile video, Nov 2018.
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A087062 (lunar product).
Cf. A087028, A087083, A186443, A186510. See A189506 for the actual divisors.
See A067399 for the base-2 version.

(Uses programs from A087062. This crude program is valid for n <= 99.) dd2 := proc(n) local t1,t2,i,j; t1 := []; for i from 1 to 99 do for j from i to 99 do if dmul(i,j) = n then t1 := [op(t1),i,j]; fi; od; od; t1 := convert(t1,set); t2 := sort(convert(t1,list)); nops(t2); end;

A087029(n)=#A189506_row(n) \\ To be optimized. - M. F. Hasler, Nov 15 2018

More terms from David Applegate, Nov 07 2003

Minor edits by M. F. Hasler, Nov 15 2018

A087636 Number of n-digit lunar primes.

Original entry on oeis.org

0, 18, 81, 1539, 20457, 242217, 2894799, 33535839, 381591711

Offset: 1

Marc LeBrun and N. J. A. Sloane, Oct 26 2003

Although a(1) through a(6) are divisible by 9, a(7) is not.

D. Applegate, C program for lunar arithmetic and number theory
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arxiv:1107.1130 [math.NT], July 2011. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun, and N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
Benjamin Baily, Justine Dell, Henry L. Fleischmann, Faye Jackson, Steven J. Miller, Ethan Pesikoff, and Luke Reifenberg, Irreducibility over the max-min semiring, arXiv:2111.09786 [math.CO], 2021.
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A087062 (lunar product), A087097 (lunar primes), A087638 (partial sums).

A87636=[]; A087636(n)={while(#A87636A087097(k)); A87636[n]} \\ Store results in array A87636 to avoid re-calculation. - M. F. Hasler, Nov 15 2018

a(6)-a(9) from David Applegate, Nov 07 2003

A087052 Lunar triangular numbers: 0+1+2+3+...+n, where + is lunar addition.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 199, 199, 199, 199, 199, 199, 199, 199, 199, 199, 199, 199, 199, 199, 199, 199, 199, 199, 199, 199, 199

Offset: 0

Marc LeBrun and N. J. A. Sloane, Oct 19 2003

nonn

Differs from A087121 after 100 terms.

If duplicates are removed we get A051885. - N. J. A. Sloane, Jan 25 2011

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A051885.

(Continuing from A087062) dt := proc(n) local i,t1; t1 := 0; for i from 1 to n do t1 := dadd(t1,i); od: t1; end;

A087028 Number of bounded (<=n) lunar divisors of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 9, 9, 9, 8, 7, 6, 5, 4, 3, 2, 8, 8, 8, 8, 7, 6, 5, 4, 3, 2, 7, 7, 7, 7, 7, 6, 5, 4, 3, 2, 6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 5, 5, 5, 5, 5, 5, 5, 4, 3, 2, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 19, 10, 9, 8, 7, 6, 5, 4, 3, 2, 100, 91, 17, 15, 13, 11, 9, 7, 5, 3, 25, 25, 81, 22, 19, 16, 13, 10, 7, 4, 22, 22, 22, 64, 19, 16, 13, 10, 7, 4, 19, 19, 19, 19, 49, 16, 13, 10, 7, 4, 16, 16, 16, 16, 16, 36, 13, 10, 7, 4, 13, 13, 13, 13, 13, 13, 25, 10, 7, 4, 10, 10, 10, 10, 10, 10, 10, 16, 7, 4, 7, 7, 7, 7, 7, 7, 7, 7, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 17

Offset: 1

Marc LeBrun and N. J. A. Sloane, Oct 19 2003

Number of d, 1 <= d <= n, such that there exists an e, 1 <= e <= n, with d*e = n, where * is lunar multiplication.

			The 10 divisors of 10 <= 10 are 1, 2, ..., 9, 10.
a(100) = 19, since the lunar divisors of 100 <= 100 are 1, 2, ..., 9, 10, 20, ..., 90, 100.

D. Applegate, Table of n, a(n) for n = 1..100000
D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A087029, A087082.

(Uses programs from A087062) dd1 := proc(n) local t1,t2,i,j; t1 := []; for i from 1 to n do for j from i to n do if dmul(i,j) = n then t1 := [op(t1),i,j]; fi; od; od; t1 := convert(t1,set); t2 := sort(convert(t1,list)); nops(t2); end;

A087638 Number of lunar primes with <= n digits.

Original entry on oeis.org

0, 18, 99, 1638, 22095, 264312, 3159111, 36694950, 418286661

Offset: 1

Marc LeBrun and N. J. A. Sloane, Oct 26 2003

Partial sums of A087636. - M. F. Hasler, Nov 15 2018

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arxiv:1107.1130 [math.NT], July 2011. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A087062 (lunar product), A087097 (lunar primes), A087636 (#{n-digit primes}).

A087638(n)=sum(k=2,n,A087636(k)) \\ M. F. Hasler, Nov 15 2018

a(6)-a(9) from David Applegate, Nov 07 2003

A261684 Array T(n,k) = lunar product n*k (n >= 0, k >= 0) read by antidiagonals.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 0, 10, 2, 3, 4, 5, 5, 4, 3, 2, 10, 0, 0, 11, 10, 3, 4, 5, 6, 5, 4, 3, 10, 11, 0

Offset: 0

N. J. A. Sloane, Sep 06 2015

See A087061 for definition. Note that 0+x = x and 9*x = x for all x.

			Lunar multiplication table begins:
0 0 0 0 0 0 ...
0 1 1 1 1 1 ...
0 1 2 2 2 2 ...
0 1 2 3 3 3 ...
0 1 2 3 4 4 ...
0 1 2 3 4 5 ...
....

N. J. A. Sloane, Table of n, a(n) for n = 0..20099
D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Brady Haran and N. J. A. Sloane, Primes on the Moon (Lunar Arithmetic), Numberphile video, Nov 2018.
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A087061 (addition).
See A087062 for a version that excludes the zero row and column.
Similar to but different from A003983.

# convert decimal to string:
rec := proc(n) local t0,t1,e,l; if n <= 0 then RETURN([[0],1]); fi; t0 := n mod 10; t1 := (n-t0)/10; e := [t0]; l := 1; while t1 <> 0 do t0 := t1 mod 10; t1 := (t1-t0)/10; l := l+1; e := [op(e),t0]; od; RETURN([e,l]); end;
# convert string to decimal:
cer := proc(ep) local i,e,l,t1; e := ep[1]; l := ep[2]; t1 := 0; if l <= 0 then RETURN(t1); fi; for i from 1 to l do t1 := t1+10^(i-1)*e[i]; od; RETURN(t1); end;
# lunar addition:
dadd := proc(m,n) local i,r1,r2,e1,e2,l1,l2,l,l3,t0; r1 := rec(m); r2 := rec(n); e1 := r1[1]; e2 := r2[1]; l1 := r1[2]; l2 := r2[2]; l := max(l1,l2); l3 := min(l1,l2); t0 := array(1..l); for i from 1 to l3 do t0[i] := max(e1[i],e2[i]); od; if l>l3 then for i from l3+1 to l do if l1>l2 then t0[i] := e1[i]; else t0[i] := e2[i]; fi; od; fi; cer([t0,l]); end;
# lunar multiplication:
dmul := proc(m,n) local k,i,j,r1,r2,e1,e2,l1,l2,l,t0; r1 := rec(m); r2 := rec(n); e1 := r1[1]; e2 := r2[1]; l1 := r1[2]; l2 := r2[2]; l := l1+l2-1; t0 := array(1..l); for i from 1 to l do t0[i] := 0; od; for i from 1 to l2 do for j from 1 to l1 do k := min(e2[i],e1[j]); t0[i+j-1] := max(t0[i+j-1],k); od; od; cer([t0,l]); end;
# to produce the b-file:
M:=199; c:=0; for n from 0 to M do for k from 0 to n do lprint(c,dmul(n-k,k)); c:=c+1; od: od:

A343042 Array T(n, k), n, k >= 0, read by antidiagonals; lunar multiplication table for the factorial base.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 6, 3, 0, 0, 2, 8, 8, 2, 0, 0, 3, 6, 9, 6, 3, 0, 0, 6, 8, 8, 8, 8, 6, 0, 0, 7, 24, 9, 12, 9, 24, 7, 0, 0, 8, 26, 30, 14, 14, 30, 26, 8, 0, 0, 9, 30, 33, 24, 15, 24, 33, 30, 9, 0, 0, 8, 32, 32, 26, 30, 30, 26, 32, 32, 8, 0

Offset: 0

Rémy Sigrist, Apr 05 2021

To compute T(n, k):
- write the factorial base representations of n and of k on two lines, right aligned,
- to "multiply" two digits: take the smallest,
- to "add" two digits: take the largest,
- for example, for T(13, 14):
     12   ->   2 0 1
     14   -> x 2 1 0
             -------
               0 0 0
             1 0 1
         + 2 0 1
         -----------
           2 1 1 1 0  ->  272 = T(13, 14)
See A343040 for the corresponding addition table.

			Array T(n, k) begins:
  n\k|  0  1   2   3   4   5    6    7    8    9   10   11   12
  ---+---------------------------------------------------------
    0|  0  0   0   0   0   0    0    0    0    0    0    0    0
    1|  0  1   2   3   2   3    6    7    8    9    8    9    6
    2|  0  2   6   8   6   8   24   26   30   32   30   32   24
    3|  0  3   8   9   8   9   30   33   32   33   32   33   30
    4|  0  2   6   8  12  14   24   26   30   32   36   38   48
    5|  0  3   8   9  14  15   30   33   32   33   38   39   54
    6|  0  6  24  30  24  30  120  126  144  150  144  150  120
    7|  0  7  26  33  26  33  126  127  152  153  152  153  126
    8|  0  8  30  32  30  32  144  152  150  152  150  152  144
    9|  0  9  32  33  32  33  150  153  152  153  152  153  150
   10|  0  8  30  32  36  38  144  152  150  152  156  158  168
   11|  0  9  32  33  38  39  150  153  152  153  158  159  174
   12|  0  6  24  30  48  54  120  126  144  150  168  174  240

Rémy Sigrist, Table of n, a(n) for n = 0..10010
Rémy Sigrist, PARI program for A343042
Index entries for sequences related to dismal (or lunar) arithmetic
Index entries for sequences related to factorial base representation

Cf. A087062, A343040, A343046.

PARI
```
See Links section.
```

T(n, k) = T(k, n).
T(m, T(n, k)) = T(T(m, n), k).
T(n, 0) = 0.

A343046 Array T(n, k), n, k >= 0, read by antidiagonals; lunar multiplication table for the primorial base.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 6, 3, 0, 0, 2, 8, 8, 2, 0, 0, 3, 6, 9, 6, 3, 0, 0, 6, 8, 8, 8, 8, 6, 0, 0, 7, 30, 9, 12, 9, 30, 7, 0, 0, 8, 32, 36, 14, 14, 36, 32, 8, 0, 0, 9, 36, 39, 30, 15, 30, 39, 36, 9, 0, 0, 8, 38, 38, 32, 36, 36, 32, 38, 38, 8, 0

Offset: 0

Rémy Sigrist, Apr 05 2021

To compute T(n, k):
- write the primorial base representations of n and of k on two lines, right aligned,
- to "multiply" two digits: take the smallest,
- to "add" two digits: take the largest,
- for example, for T(9, 10):
      9   ->   1 1 1
     10   -> x 1 2 0
             -------
               0 0 0
             1 1 1
         + 1 1 1
         -----------
           1 1 1 1 0  ->  248 = T(9, 10)
See A343044 for the corresponding addition table.

			Array T(n, k) begins:
  n\k|  0  1   2   3   4   5    6    7    8    9   10   11   12
  ---+---------------------------------------------------------
    0|  0  0   0   0   0   0    0    0    0    0    0    0    0
    1|  0  1   2   3   2   3    6    7    8    9    8    9    6  ->  A328841
    2|  0  2   6   8   6   8   30   32   36   38   36   38   30
    3|  0  3   8   9   8   9   36   39   38   39   38   39   36
    4|  0  2   6   8  12  14   30   32   36   38   42   44   60
    5|  0  3   8   9  14  15   36   39   38   39   44   45   66
    6|  0  6  30  36  30  36  210  216  240  246  240  246  210
    7|  0  7  32  39  32  39  216  217  248  249  248  249  216
    8|  0  8  36  38  36  38  240  248  246  248  246  248  240
    9|  0  9  38  39  38  39  246  249  248  249  248  249  246
   10|  0  8  36  38  42  44  240  248  246  248  252  254  270
   11|  0  9  38  39  44  45  246  249  248  249  254  255  276
   12|  0  6  30  36  60  66  210  216  240  246  270  276  420

Rémy Sigrist, Table of n, a(n) for n = 0..10010
Rémy Sigrist, PARI program for A343046
Index entries for sequences related to dismal (or lunar) arithmetic
Index entries for sequences related to primorial base

Cf. A087062, A235168, A328841, A343042, A343044, A343047.

PARI
```
See Links section.
```

T(n, k) = T(k, n).
T(m, T(n, k)) = T(T(m, n), k).
T(n, 0) = 0.
T(n, 1) = A328841(n).
T(n, n) = A343047(n).

A087082 Take bounded lunar divisors of n as defined in A087028, add them using normal addition. See A087121 for their lunar sum.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 55, 56, 56, 55, 53, 50, 46, 41, 35, 28, 64, 65, 66, 65, 63, 60, 56, 51, 45, 38, 72, 73, 74, 75, 73, 70, 66, 61, 55, 48, 79, 80, 81, 82, 83, 80, 76, 71, 65, 58, 85, 86, 87, 88, 89, 90, 86, 81, 75, 68, 90, 91, 92, 93, 94, 95, 96, 91, 85, 78

Offset: 1

Marc LeBrun and N. J. A. Sloane, Oct 19 2003

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A087061, A087062, A087028, A087083.

More terms from David Applegate, Nov 07 2003

cp's OEIS Frontend

A004197 Triangle read by rows. T(n, k) = n - k if n - k < k, otherwise k.

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A087029 Number of lunar divisors of n (unbounded version).

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A087636 Number of n-digit lunar primes.

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A087052 Lunar triangular numbers: 0+1+2+3+...+n, where + is lunar addition.

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Maple

A087028 Number of bounded (<=n) lunar divisors of n.

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Maple

A087638 Number of lunar primes with <= n digits.

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PARI

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A261684 Array T(n,k) = lunar product n*k (n >= 0, k >= 0) read by antidiagonals.

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A343042 Array T(n, k), n, k >= 0, read by antidiagonals; lunar multiplication table for the factorial base.

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