A212849 Numbers whose sum of prime factors (counted with multiplicity) is a triangular number.

1, 3, 8, 9, 21, 25, 26, 30, 32, 36, 38, 44, 68, 86, 105, 106, 112, 115, 125, 126, 138, 150, 155, 160, 164, 178, 180, 186, 187, 192, 195, 203, 206, 208, 216, 231, 234, 243, 266, 275, 290, 299, 302, 305, 323, 330, 338, 343, 348, 352, 365, 366, 380, 396, 404, 413

Offset: 1

Author

Jonathan Vos Post, May 28 2012

Keywords

• nonn
• easy

Comments

This is to A212831 Numbers whose sum of prime factors is a square (counted with multiplicity) as A000290 squares are to A000217 triangular numbers.

Examples

			sopfr(21) = sum of primes dividing 21 (with repetition) = 10, which is the  4th triangular number, so 21 is in this sequence.
The number 1 is here because the sum of its prime factors is 0, which is a triangular number.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000217, A001414, A212831.

Programs

Mathematica

triangularQ[n_] := IntegerQ[Sqrt[1 + 8*n]]; fQ[n_] := Module[{p, e}, {p, e} = Transpose[FactorInteger[n]]; triangularQ[Dot[p, e]]]; Join[{1}, Select[Range[2, 500], fQ]] (* T. D. Noe, May 30 2012 *)

PARI

sopfr(n) = my(f=factor(n)); sum(k=1, matsize(f)[1], f[k, 1]*f[k, 2]); \\ A001414
isok(n) = ispolygonal(sopfr(n), 3); \\ Michel Marcus, May 02 2018

Formula

{k such that A001414(k) = sopfr(k) is in A000217}.