%I #7 Mar 30 2012 18:50:59
%S 0,0,1,0,1,0,1,0,0,2,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,2,1,0,0,
%T 0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,
%U 1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0
%N Number of prime powers p^e with e>1 and 0<prime(n)-p^e<p.
%C a(A049084(A074267(n))) > 0;
%C a(31)=2, what is the next value greater than 1?.
%H R. Zumkeller, <a href="/A138363/b138363.txt">Table of n, a(n) for n = 1..10000</a>
%e A000040(10)=29: a(10) = #{4+5^2, 2+3^3} = 2.
%t f[n_] := Block[{c = 0, j, k = 1, p = Prime@ n, q}, j = 1 + PrimePi@ Sqrt@ p; While[k < j, q = Prime@ k; If[p < q + q^Floor@ Log[q, p], c++ ]; k++ ]; c]; Array[f, 105]
%K nonn
%O 1,10
%A _Reinhard Zumkeller_, Mar 16 2008
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