%I #3 Mar 30 2012 18:50:59
%S 10,31,14774,14775,65686,110128,110129,110130,110131,110132,110133,
%T 110134,110135,110136,110137,165952,165953,165954,165955,165956,
%U 165957,165958,304841,304842,304843,304844,304845,304846,304847
%N Indices of the primes p for which the number of representations of p as the sum of a perfect prime power (A025475: q^e with e>1) and an integer k which is less than q exceeds one.
%C Where A138363 exceeds 1.
%e A000040(10)=29; A138363(10) = #{4+5^2, 2+3^3} = 2.
%t f[n_] := Block[{c = 0, e, 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]; lst = {}; Do[ If[f@n > 1, AppendTo[lst, n]; Print[Prime@n]], {n, 25*10^5}]
%Y Cf. A138363, A074267.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_ & _Robert G. Wilson v_, Mar 23 2008