A130871 Numbers k such that the sum of the prime factors with multiplicity of k divides k+1.

15, 35, 44, 54, 90, 95, 119, 143, 209, 287, 319, 323, 328, 351, 377, 390, 423, 527, 559, 608, 779, 899, 923, 924, 989, 1007, 1189, 1199, 1280, 1343, 1349, 1715, 1763, 1805, 1825, 1919, 2000, 2159, 2448, 2507, 2755, 2759, 2847, 2911, 3008

Offset: 1

Author

J. M. Bergot, Jul 24 2007

Keywords

• easy
• nonn

Examples

			90=2*3*3*5 with sum 2+3+3+5=13, 7*13=91, so 90 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001414, A036844.

Programs

Mathematica

Select[Range[2, 10000], IntegerQ[(# + 1)/Sum[FactorInteger[ # ][[i,1]] *FactorInteger[ # ][[i, 2]], {i, 1, Length[FactorInteger[ # ]]}]] &] (* Stefan Steinerberger, Jul 26 2007 *)

Formula

List the factors of n with multiplicity to see if their sum divides the following number n+1.

Extensions

Corrected and extended by Stefan Steinerberger, Jul 26 2007