A080743 Array read by rows in which n-th row lists orders of elements of Symm(n) that are not orders of elements of Symm(n-1) (6th row is empty, written as 0 by convention).

1, 2, 3, 4, 5, 6, 0, 7, 10, 12, 8, 15, 9, 14, 20, 21, 30, 11, 18, 24, 28, 35, 42, 60, 13, 22, 36, 40, 33, 45, 70, 84, 26, 44, 56, 105, 16, 39, 55, 63, 66, 90, 120, 140, 17, 52, 72, 210, 65, 77, 78, 110, 126, 132, 168, 180, 19, 34, 48, 88, 165, 420, 51, 91, 99, 130, 154, 156, 220

Offset: 1

Author

N. J. A. Sloane, Mar 08 2003

Keywords

• nonn
• tabf
• look
• easy

Comments

A051613 gives number of elements in n-th row.

Examples

			1;
2;
3;
4;
5, 6;
0;
7, 10, 12;
8, 15;
...
		

Links

• Alois P. Heinz, Rows n = 1..100, flattened
• J. Bamberg, G. Cairns and D. Kilminster, The crystallographic restriction, permutations and Goldbach's conjecture, Amer. Math. Monthly, 110 (March 2003), 202-209.

Crossrefs

Cf. A008475, A051613, A080744, A051703.

Programs

Maple

b:= proc(n) option remember; `if`(n<3, {n},
      {n, seq(map(x-> ilcm(x, i), b(n-i))[], i=2..n-1)}
       minus {seq(b(i)[], i=1..n-1)})
    end:
T:= proc(n) local l; l:= [b(n, n)[]];
      `if`(nops(l)=0, 0, sort(l)[])
    end:
seq(T(n), n=1..20);  # Alois P. Heinz, Feb 15 2013

Mathematica

b[n_, i_] := b[n, i] = Module[{p}, p = If[i<1, 1, Prime[i]]; If[n == 0, 1, If[i<1 || n<0, 0, Max[Join[{b[n, i-1]}, Table[p^j*b[n-p^j, i-1], {j, 1, Log[p, n]}]]]]] ]; T[1] = {1}; T[6] = {0}; T[n_] := Reap[For[m = n, m <= b[n, PrimePi[n]], m++,  If[n == Total[Power @@@ FactorInteger[m]], Sow[m]]]][[2, 1]]; Table[T[n], {n, 1, 20}] // Flatten (* Jean-François Alcover, Feb 26 2015, after Alois P. Heinz *)

Formula

n-th row = set of m such that A008475(m) = n, or 0 if no such m exists.

Extensions

More terms from Vladeta Jovovic, Mar 12 2003