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

1,1

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.

Links

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

Example

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.

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 *)

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).

Sequence in context: A209339 A212500 A302198 * A367775 A245305 A152450

Adjacent sequences: A279827 A279828 A279829 * A279831 A279832 A279833

Keyword

nonn

Author

Daniel Sterman, Dec 20 2016

Extensions

Corrected and extended by Davin Park, Dec 27 2016

Status

approved