A279830 a(n) = the least integer that is centered polygonal in exactly n ways.

4, 7, 37, 31, 91, 181, 211, 421, 631, 1891, 1261, 2521, 6931, 18481, 20791, 13861, 27721, 41581, 83161, 138601, 245701, 235621, 180181, 556921, 360361, 540541, 1670761, 1081081, 1413721, 2702701, 2162161, 6486481, 3063061, 8288281, 13430341, 6846841, 10270261, 6126121

Offset: 1

Author

Daniel Sterman, Dec 20 2016

Keywords

• nonn

Comments

a(n) has exactly n representations as a centered r-gonal number P(r,m) = 1 + r*m*(m+1)/2, with m > 1, r > 0.

a(n) appears n+1 times in A101321, due to the second column containing every positive integer.

a(n)-1 is the first appearance of n+1 in A007862.

Examples

			a(4)=31, because 31 is a centered triangular number (A005448), a centered pentagonal number (A005891), a centered decagonal number (A062786), and a central polygonal number (A002061). No number less than 31 has 4 representations.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..143

Crossrefs

Cf. A007862 (see alternative definition: the number of ways to represent n+1 as a centered polygonal number).

Cf. A063778 (the equivalent for polygonal numbers).

Subset of A275340 (the list of nontrivial centered polygonal numbers).

Subset of A101321 (centered polygonal numbers read by antidiagonals).

Programs

Mathematica

f[n_] := Length@Select[Divisors[2 n - 2], IntegerQ@Sqrt[1 + 4 #] &] - 1;
Do[If[IntegerQ[A279830[f[i]]], , A279830[f[i]] = i], {i, 10000}];
A279830 /@ Range[13]
(* Davin Park, Dec 28 2016 *)

Extensions

Corrected and extended by Davin Park, Dec 27 2016