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

3,1

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.

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A176210 A187824 A357081 * A162552 A133575 A230113

Adjacent sequences: A177025 A177026 A177027 * A177029 A177030 A177031

Keyword

nonn,tabf,easy

Author

Vladimir Shevelev, May 01 2010

Status

approved