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A164865
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Sum of the distinct semiprime divisors of the n-th number with two or more distinct semiprime divisors.
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2
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10, 15, 14, 10, 18, 31, 19, 14, 41, 26, 24, 10, 35, 30, 15, 18, 35, 30, 61, 38, 59, 19, 40, 42, 71, 14, 45, 26, 40, 50, 10, 63, 42, 39, 91, 30, 71, 19, 87, 18, 101, 62, 48, 35, 66, 50, 101, 65, 24, 38, 121, 63, 19, 70, 78, 56, 42, 60, 113, 75, 14, 15, 86, 103, 45, 129, 66, 90
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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