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

1,1

Links

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

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A001414, A036844.

Sequence in context: A238605 A233561 A114988 * A332378 A244969 A090196

Adjacent sequences: A130868 A130869 A130870 * A130872 A130873 A130874

Keyword

easy,nonn

Author

J. M. Bergot, Jul 24 2007

Extensions

Corrected and extended by Stefan Steinerberger, Jul 26 2007

Status

approved