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A177028 Irregular table: row n contains values k (in descending order) for which n is a k-gonal number 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

Every row begins with n and contains all values of k for which n is 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 in 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 37 we have row {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 *)

CROSSREFS

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

Sequence in context: A004484 A176210 A187824 * A162552 A133575 A230113

Adjacent sequences:  A177025 A177026 A177027 * A177029 A177030 A177031

KEYWORD

nonn,tabf

AUTHOR

Vladimir Shevelev, May 01 2010

STATUS

approved

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Last modified October 21 04:50 EDT 2014. Contains 248373 sequences.