A138363 Number of prime powers p^e with e>1 and 0<prime(n)-p^e<p.

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

1,10

Comments

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

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

Links

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

Example

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

Mathematica

 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]

Crossrefs

Sequence in context: A319532 A317576 A070205 * A080225 A122841 A326075

Adjacent sequences: A138360 A138361 A138362 * A138364 A138365 A138366

Keyword

nonn

Author

Reinhard Zumkeller, Mar 16 2008

Status

approved