OFFSET
1,1
COMMENTS
The sum of semiprime divisors of all k such that A086971(k) > 1.
This sum is prime for k = 30, 36, 60, 72, and infinitely more values (every prime power of every primitive element).
FORMULA
EXAMPLE
a(1) = 10 because the 1st number with 2 or more distinct semiprime divisors is k=12=A102467(2), as A001358(1) = 4, 4|12, A001358(2) = 6, 6|12, and 4+6 = 10.
a(6) = 31 because the 6th number with multiple distinct semiprime factors is k=30=A102467(7), the semiprimes 6, 10, and 15 divide 30, and 6 + 10 + 15 = 31.
MAPLE
isA001358 := proc(n) RETURN( numtheory[bigomega](n) =2 ) ; end:
A086971 := proc(n) local a, d; a := 0 ; for d in numtheory[divisors](n) do if isA001358(d) then a := a+1; fi; od; a ; end:
A102467 := proc(n) local a; if n = 1 then 1; else for a from procname(n-1)+1 do if A086971(a) >= 2 then RETURN(a) ; fi; od: fi; end:
A076290 := proc(n) local a, d; a := 0 ; for d in numtheory[divisors](n) do if isA001358(d) then a := a+d; fi; od; a ; end:
A164865 := proc(n) A076290( A102467(n+1)) ; end: seq(A164865(n), n=1..120) ; # R. J. Mathar, Aug 31 2009
MATHEMATICA
sdsd[n_]:=Module[{spd=Select[Divisors[n], PrimeOmega[#]==2&]}, If[ Length[ spd]> 1, Total[spd], 0]]; DeleteCases[Array[sdsd, 200], 0] (* Harvey P. Dale, Oct 29 2015 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Aug 28 2009
EXTENSIONS
Corrected and extended by R. J. Mathar, Aug 31 2009
STATUS
approved