A131564 Let spm(n) be the sum of all prime factors of n counted with multiplicities (A001414); sequence gives numbers n such that spm(n+spm(n)) divides both n and n+spm(n).

60, 70, 240, 2079, 2408, 2928, 3000, 3125, 4250, 6748, 15560, 19018, 19805, 22448, 24508, 28560, 29412, 31416, 33160, 39347, 43868, 44268, 46025, 53928, 55298, 70438, 78387, 80236, 81655, 91238, 94800, 96824, 106134, 117952

Offset

1,1

Links

Table of n, a(n) for n=1..34.

Example

Take 60, having sum of prime factors 2+2+3+5=12 and add that 12 to 60 to get 72, having the sum of its prime factors 2+2+2+3+3=12. We see that this 12 divides both 60 and 72.
For 2408, the sum of prime factors is 2+2+2+7+43=56, added to 2408 gives 2464, with sum of prime factors being 2+2+2+2+2+7+11=28; this 28 divides both 2408 and 2464.

Mathematica

spm[n_]:=Total[Times@@@FactorInteger[n]]; Select[Range[117952], Divisible[#, spm[#+spm[#]]]&&Divisible[#+spm[#], spm[#+spm[#]]]&] (* James C. McMahon, Feb 25 2025 *)

Crossrefs

Sequence in context: A216828 A345997 A382837 * A036457 A030630 A068350

Adjacent sequences: A131561 A131562 A131563 * A131565 A131566 A131567

Keyword

nonn

Author

J. M. Bergot, Aug 27 2007

Extensions

Edited by Olivier Gérard, Sep 27 2007

Status

approved