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 A144586 a(n) = odd and nonprime sum of prime factors of composite(k) = A002808(k). 0

%I #13 Oct 19 2015 04:05:49

%S 9,9,9,15,9,21,15,25,33,21,39,45,27,49,15,55,15,33,63,35,15,15,69,75,

%T 15,25,81,15,45,85,25,91,15,51,15,99,21,105,21,57,15,111,115,21,35,21,

%U 63,15,65,129,25,35,133,25,21,141,75,27,77,153,27,25,159,165,21,87,169,27

%N a(n) = odd and nonprime sum of prime factors of composite(k) = A002808(k).

%e At k=7, A002808(k) = 14 = 2*7, and 2 + 7 = 9 (an odd nonprime), and k=7 is the smallest index for which this occurs, so a(1)=9.

%e At k=11, A002808(k) = 20 = 2*2*5, and 2 + 2 + 5 = 9 (an odd nonprime), and k=11 is the 2nd smallest index for which this occurs, so a(2)=9.

%e At k=14, A002808(k) = 24 = 2*2*2*3, and 2 + 2 + 2 + 3 = 9 (an odd nonprime), and k=24 is the 3rd smallest index for which this occurs, so a(3)=9.

%e At k=16, A002808(k) = 26 = 2*13 and 2 + 13 = 15 (an odd nonprime), and k=26 is the 4th smallest index for which this occurs, so a(4)=15, etc.

%p # _R. J. Mathar_, May 01 2010: (Start)

%p pss := proc(n) a := 0 ; for d in ifactors(n)[2] do a := a+ op(2,d)*op(1,d) ; end do: a ; end proc:

%p A002808 := proc(n) if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then return a; end if; end do: end if; end proc:

%p A046343 := proc(n) pss(A002808(n)) ; end proc:

%p for k from 1 to 800 do a := A046343(k) ; if not isprime(a) and type(a,'odd') then printf("%d,",a) ; end if; end do: # (End)

%Y Cf. A002808, A141468.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Jan 04 2009

%E Corrected at two or more places and extended by _R. J. Mathar_, May 01 2010

%E Example section edited by _Jon E. Schoenfield_, Oct 18 2015

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Last modified September 19 13:45 EDT 2024. Contains 376012 sequences. (Running on oeis4.)