A316676 Ordered set of products (P_s(k) + 1)*(P_s'(k') + 1), s,s' >= 3, k,k' in {3,4} with nontrivial polygonal numbers P_s(k).

49, 70, 77, 91, 100, 110, 112, 119, 121, 130, 133, 143, 154, 160, 161, 169, 170, 175, 176, 187, 190, 196, 203, 208, 209, 217, 220, 221, 230, 238, 242, 245, 247, 250, 253, 256, 259, 272, 275, 280, 286, 287, 289, 290, 299, 301, 304, 308, 310, 319, 322, 323, 325, 329, 340, 341, 343, 350, 352, 361, 364

Offset: 1

Author

Ralf Steiner, Jul 10 2018

Keywords

• nonn

Comments

Conjecture: All odd numbers d >= 17 excluding d in {P_s(k), s >= 3, k >= 5; P_s(k) - 1, s >= 3, k >= 4; a(n)} are accurate the primes p = d >= 17.

Crossrefs

Cf. A090466 (nontrivial polygonal numbers).

Programs

Mathematica

pn[s_, k_] := s (k - 1) k/2 - (k - 1)^2 + 1;
lst = {}; Do[n = (pn[s, k] + 1) (pn[ss, ks] + 1);
lst = Union[lst, {n}], {s, 3, 20}, {ss, 3, 20}, {k, 3, 4}, {ks, 3,
  4}]; Take[lst, 70]