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%I #6 Oct 15 2013 22:31:24
%S 0,6,8,0,10,18,14,14,0,26,28,20,24,42,0,28,27,39,51,44,32,37,32,66,42,
%T 39,65,71,60,56,51,93,40,68,51,72,89,51,89,57,65,128,71,76,0,60,109,
%U 95,71,109,150,83,93,105,71,128,143,90,95,175,79,99,89,138,182,82,128,96
%N Sigma of n-th composite number equals a(n)-th composite number if it is also a composite or equals zero if sigma[c] is prime.
%F a(n)=G[sigma[c[n]]]=A065855[A000203[A002808(n)]]]= A065855[A073255[n]] if sigma[c]=A000203[A002808(n)]] is composite and a(n)=0 if A073255[n]=A000203[A002808(n)]] is prime.
%e n=1: c[1]=4, sigma[4]=1+2+4=7 prime, a(1)=0; n=10: c[10]=18, sigma[18]=1+2+3+6+9+18=39 composite and 39 is the 26th composite number, so a(10)=26.
%t c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x] G[x_] := x-PrimePi[x]-1 Do[s=c[n]; s1=DivisorSigma[1, s]; s2=G[s1]; If[PrimeQ[s1], Print[0]]; If[ !PrimeQ[s1], Print[s2]], {n, 1, 128}]
%Y Cf. A065855, A000203, A002808, A073255.
%K nonn
%O 1,2
%A _Labos Elemer_, Aug 06 2002
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