A177028 Irregular table: row n contains values k (in descending order) for which n is a k-gonal number.

3, 4, 5, 6, 3, 7, 8, 9, 4, 10, 3, 11, 12, 5, 13, 14, 15, 6, 3, 16, 4, 17, 18, 7, 19, 20, 21, 8, 3, 22, 5, 23, 24, 9, 25, 4, 26, 27, 10, 28, 6, 3, 29, 30, 11, 31, 32, 33, 12, 34, 7, 35, 5, 36, 13, 4, 3, 37, 38, 39, 14, 40, 8, 41, 42, 15

Offset: 3

Author

Vladimir Shevelev, May 01 2010

Keywords

• nonn
• tabf
• easy

Comments

Every row begins with n and contains all values of k for which n is a k-gonal number.

The cardinality of row n is A177025(n). In particular, if n is prime, then row n contains only n.

Examples

			The table starts with row n=3 as:
3;
4;
5;
6, 3;
7;
8;
9, 4;
10, 3;
11;
12, 5;
13;
14;
15, 6, 3;
16, 4;
17;
18, 7;
19;
20;
Before n=37, we have row n=36: {36, 13, 4, 3}. Thus 36 is k-gonal for k=3, 4, 13 and 36.
		

Links

• T. D. Noe, Rows n = 3..1000, flattened

Crossrefs

Cf. A063778, A090467, A139600, A177025, A176948, A176774, A176775.

Programs

Maple

P := proc(n,k) n/2*((k-2)*n-k+4) ;end proc:
A177028 := proc(n) local k ,j,r,kg ; r := {} ; for k from n to 3 by -1 do for j from 1 do kg := P(j,k) ; if kg = n then r := r union {k} ;elif kg > n then break ; end if; end do; end do: sort(convert(r,list),`>`) ; end proc:
for n from 3 to 20 do print(A177028(n)) ; end do: # R. J. Mathar, Apr 17 2011

Mathematica

nn = 100; t = Table[{}, {nn}]; Do[n = 2; While[p = n*(4 - 2*n - r + n*r)/2; p <= nn, AppendTo[t[[p]], r]; n++], {r, 3, nn}]; Flatten[Reverse /@ t] (* T. D. Noe, Apr 18 2011 *)

PARI

row(n) = my(list = List()); for (k=3, n, if (ispolygonal(n, k), listput(list, k))); Vecrev(list); \\ Michel Marcus, Mar 19 2021

PARI

row(n)=my(v=List());fordiv(2*n,k, if(k<2,next); if(k==n, break); my(s=(2*n/k-4+2*k)/(k-1)); if(denominator(s)==1, listput(v,s))); Vec(v) \\ Charles R Greathouse IV, Mar 19 2021