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 A279830 a(n) = the least integer that is centered polygonal in exactly n ways. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 * A245305 A152450 A059213 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

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Last modified July 2 04:56 EDT 2022. Contains 354985 sequences. (Running on oeis4.)