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 A164865 Sum of the distinct semiprime divisors of the n-th number with two or more distinct semiprime divisors. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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). LINKS Table of n, a(n) for n=1..68. FORMULA a(n) = Sum_(k|A102467(n) and k in A001358) k. a(n) = A076290( A102467(n+1)). - R. J. Mathar, Aug 31 2009 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 Cf. A001358, A068318, A086971, A102467. Sequence in context: A063582 A074391 A324527 * A253594 A330698 A342593 Adjacent sequences: A164862 A164863 A164864 * A164866 A164867 A164868 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Aug 28 2009 EXTENSIONS Corrected and extended by R. J. Mathar, Aug 31 2009 STATUS approved

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Last modified August 9 02:18 EDT 2024. Contains 375024 sequences. (Running on oeis4.)