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%I #3 Feb 11 2014 19:05:30
%S 0,0,1,1,1,4,1,4,1,5,1,7,1,6,5,5,1,9,1,9,6,7,1,13,1,8,5,11,1,16,1,12,
%T 7,10,6,19,1,10,7,18,1,19,1,15,12,12,1,24,3,16,9,16,1,23,8,21,11,15,1,
%U 33,1,14,16,18,8,26,1,19,10,25,1,35,1,19,18,23,7,30,1,31,14,18,1,39,10,19
%N Number of primes between sigma(n) and phi(n).
%C a(n) appears to be nonzero for n > 2.
%e sigma(6) = 12 and phi(6) = 2. There are 4 primes between 12 and 2 (endpoints are excluded), namely 3, 5, 7, 11. Hence a(6) = 4.
%t (*gives number of primes < n*) f[n_] := Module[{r, i}, r = 0; i = 1; While[Prime[i] < n, i++ ]; i - 1]; (*gives number of primes between m and n with endpoints excluded*) g[m_, n_] := Module[{r}, r = f[m] - f[n]; If[PrimeQ[m], r = r - 1]; If[PrimeQ[n], r = r - 1]; r]; Table[g[DivisorSigma[1, n], EulerPhi[n]], {n, 1, 100}]
%K nonn
%O 1,6
%A _Joseph L. Pe_, Sep 24 2002