

A177028


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


8



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
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OFFSET

3,1


COMMENTS

Every row begins with n and contains all values of k for which n is a kgonal 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 kgonal for k=3, 4, 13 and 36.


MAPLE

P := proc(n, k) n/2*((k2)*nk+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/k4+2*k)/(k1)); 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



