A074267 -id:A074267 - cp's OEIS frontend

A138363 Number of prime powers p^e with e>1 and 0

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, 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, 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

Offset: 1

Reinhard Zumkeller, Mar 16 2008

nonn

a(A049084(A074267(n))) > 0;

a(31)=2, what is the next value greater than 1?.

			A000040(10)=29: a(10) = #{4+5^2, 2+3^3} = 2.

R. Zumkeller, Table of n, a(n) for n = 1..10000

 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]

A136335 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.

Original entry on oeis.org

10, 31, 14774, 14775, 65686, 110128, 110129, 110130, 110131, 110132, 110133, 110134, 110135, 110136, 110137, 165952, 165953, 165954, 165955, 165956, 165957, 165958, 304841, 304842, 304843, 304844, 304845, 304846, 304847

Offset: 1

Reinhard Zumkeller & Robert G. Wilson v, Mar 23 2008

nonn

Where A138363 exceeds 1.

			A000040(10)=29; A138363(10) = #{4+5^2, 2+3^3} = 2.

Cf. A138363, A074267.

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}]

cp's OEIS Frontend

A138363 Number of prime powers p^e with e>1 and 0

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