A349729 Numbers k >= 1 such that A018804(k) + A000203(k) is a triangular number.

2, 4, 5, 7, 10, 33, 34, 38, 49, 60, 92, 116, 132, 155, 159, 220, 268, 285, 315, 360, 437, 472, 579, 602, 664, 722, 835, 1254, 1269, 1320, 1336, 1348, 1436, 1786, 1797, 1890, 1996, 2016, 2024, 2050, 2115, 2163, 2344, 2427, 2455, 2595, 2710, 2961, 3497

Offset

1,1

Links

Table of n, a(n) for n=1..49.

Example

k = 10 : A018804(10) = 27, A000203(10) = 18, 27 + 18 = 45 which is a triangular number thus 10 is a term.

Mathematica

f1[p_, e_] := (p^(e + 1) - 1)/(p - 1); f2[p_, e_] := (e*(p - 1)/p + 1)*p^e; triQ[n_] := IntegerQ@Sqrt[8*n + 1]; q[n_] := triQ[Times @@ f1 @@@ (fct = FactorInteger[n]) + Times @@ f2 @@@ fct]; Select[Range[2, 3500], q] (* Amiram Eldar, Nov 27 2021 *)

Prog

(PARI) isok(k) = ispolygonal(sumdiv(k, d, k*eulerphi(d)/d) + sigma(k), 3); \\ Michel Marcus, Nov 27 2021

Crossrefs

Cf. A000203, A000217, A018804.

Sequence in context: A218931 A331518 A145734 * A027936 A082741 A288349

Adjacent sequences: A349726 A349727 A349728 * A349730 A349731 A349732

Keyword

nonn

Author

Ctibor O. Zizka, Nov 27 2021

Status

approved