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

%I A279830 #22 Jul 10 2020 14:10:16
%S A279830 4,7,37,31,91,181,211,421,631,1891,1261,2521,6931,18481,20791,13861,
%T A279830 27721,41581,83161,138601,245701,235621,180181,556921,360361,540541,
%U A279830 1670761,1081081,1413721,2702701,2162161,6486481,3063061,8288281,13430341,6846841,10270261,6126121
%N A279830 a(n) = the least integer that is centered polygonal in exactly n ways.
%C A279830 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.
%C A279830 a(n) appears n+1 times in A101321, due to the second column containing every positive integer.
%C A279830 a(n)-1 is the first appearance of n+1 in A007862.
%H A279830 Lars Blomberg, <a href="/A279830/b279830.txt">Table of n, a(n) for n = 1..143</a>
%e A279830 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.
%t A279830 f[n_] := Length@Select[Divisors[2 n - 2], IntegerQ@Sqrt[1 + 4 #] &] - 1;
%t A279830 Do[If[IntegerQ[A279830[f[i]]], , A279830[f[i]] = i], {i, 10000}];
%t A279830 A279830 /@ Range[13]
%t A279830 (* _Davin Park_, Dec 28 2016 *)
%Y A279830 Cf. A007862 (see alternative definition: the number of ways to represent n+1 as a centered polygonal number).
%Y A279830 Cf. A063778 (the equivalent for polygonal numbers).
%Y A279830 Subset of A275340 (the list of nontrivial centered polygonal numbers).
%Y A279830 Subset of A101321 (centered polygonal numbers read by antidiagonals).
%K A279830 nonn
%O A279830 1,1
%A A279830 _Daniel Sterman_, Dec 20 2016
%E A279830 Corrected and extended by _Davin Park_, Dec 27 2016