OFFSET
1,1
COMMENTS
Numbers k such that both k and k+2 are composite and each is divisible by the sum of its prime factors (counted with multiplicity).
There are at least two cases where k, k+2 and k+4 are all in A046346: k=646 and k=38104990. Are there more?
Up to 3*10^12 there is only one other such triple for k=590269019100. - Giovanni Resta, Jul 24 2019
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..2000 (terms 1..200 from Robert Israel)
EXAMPLE
a(1)=70 is a term because 70=2*5*7 is divisible by 2+5+7=14 and 72=2^3*3^2 is divisible by 2*3+3*2=12.
MAPLE
MATHEMATICA
Select[Partition[Select[Range[2, 10^6], And[! PrimeQ[#], IntegerQ[#/Total[Times @@@ FactorInteger[#]]]] &], 2, 1], Subtract @@ # == -2 &][[All, 1]] (* Michael De Vlieger, Jul 22 2019 *)
cdsQ[n_]:=CompositeQ[n]&&Divisible[n, Total[Times@@@FactorInteger[n]]]; SequencePosition[Table[If[cdsQ[n], 1, 0], {n, 872000}], {1, _, 1}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 23 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jul 22 2019
STATUS
approved