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A163871 The n-th composite plus the sum of its nontrivial divisors.

%I A163871 #10 Mar 10 2019 01:43:52
%S A163871 6,11,14,12,17,27,23,23,30,38,41,31,35,59,30,41,39,55,71,62,47,53,47,
%T A163871 90,59,55,89,95,83,77,71,123,56,92,71,97,119,71,119,79,89,167,95,103,
%U A163871 126,83,143,125,95,143,194,113,123,139,95,167,185,120,125,223,107,131,119,179
%N A163871 The n-th composite plus the sum of its nontrivial divisors.
%C A163871 Trivial divisors of a number are 1 and the number itself, see A048050.
%H A163871 Harvey P. Dale, <a href="/A163871/b163871.txt">Table of n, a(n) for n = 1..1000</a>
%F A163871 a(n) = A002808(n) + A062825(n+1).
%e A163871 a(1) = 4 + 2 =  6;
%e A163871 a(2) = 6 + 5 = 11;
%e A163871 a(3) = 8 + 6 = 14.
%p A163871 A002808 := proc(n) local resul,i ; i := 1 ; resul := 4 ; while i < n do resul := resul+1 ; while isprime(resul) do resul := resul+1 ; od ; i := i+1 ; od; RETURN(resul) ; end:
%p A163871 A048050 := proc(n) if n <= 3 then 0; else numtheory[sigma](n)-n-1 ; fi; end:
%p A163871 A163871 := proc(n) A002808(n)+A048050(A002808(n)) ; end: seq(A163871(n),n=1..80) ; # _R. J. Mathar_, Aug 11 2009
%t A163871 #+Total[Most[Rest[Divisors[#]]]]&/@Select[Range[4,200],!PrimeQ[#]&] (* _Harvey P. Dale_, Oct 28 2013 *)
%Y A163871 Cf. A027750.
%K A163871 nonn,easy
%O A163871 1,1
%A A163871 _Juri-Stepan Gerasimov_, Aug 06 2009
%E A163871 a(4) corrected by _R. J. Mathar_, Aug 11 2009