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%I #24 Feb 21 2022 09:53:39
%S 3,4,7,5,7,10,10,9,15,14,17,13,17,22,16,20,19,24,24,31,23,27,23,32,30,
%T 27,37,34,39,33,37,46,33,41,37,46,46,40,52,41,48,54,51,47,63,47,56,61,
%U 51,58,68,62,57,68,57,66,77,65,69,76,64,72,67,83,78,67,83,71,79,71,94
%N The n-th composite minus the product of the indices of the primes in its prime factorization.
%C The product of the indices of the primes (counted with multiplicity) is represented by A003963. An intermediate sequence m-A003963(m) = 0, 1, 1, 3, 2, 4, 3, 7, 5, 7, 6, ... at m=1, 2, 3, ... is defined and evaluated where m=A002808(n) is composite.
%H Harvey P. Dale, <a href="/A163830/b163830.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A002808(n) - A003963(A002808(n)).
%e At n=1, A002808(1) = 4 and A003963(4)=1, so a(1) = 4 - 1 = 3.
%e At n=2, A002808(2) = 6 and A003963(6)=2, so a(2) = 6 - 2 = 4.
%e At n=3, A002808(3) = 8 and A003963(8)=1, so a(3) = 8 - 1 = 7.
%p A002808 := proc(n) local a; 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 A163829 := proc(n) local c; c := A002808(n) ; pfs := ifactors(c)[2] ; mul( numtheory[pi](op(1,p))^op(2,p), p=pfs) ; end:
%p A163830 := proc(n) A002808(n)-A163829(n) ; end: seq(A163830(n),n=1..100) ; # _R. J. Mathar_, Aug 08 2009
%t With[{nn=100},#-Times@@(PrimePi/@Flatten[Table[#[[1]],{#[[2]]}]&/@ FactorInteger[#]])&/@Complement[Range[2,nn],Prime[Range[ PrimePi[ nn]]]]](* _Harvey P. Dale_, Mar 29 2012 *)
%Y Cf. A002808, A163515, A003963.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Aug 05 2009
%E Edited by _R. J. Mathar_, Jul 08 2009
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