A186946 The smallest integer x > 0 such that the number of prime powers p^k (k>=1) in (x/2,x] equals n.

2, 3, 5, 9, 13, 25, 29, 31, 43, 49, 71, 73, 81, 103, 109, 113, 127, 131, 139, 157, 173, 181, 191, 193, 199, 239, 241, 269, 271, 283, 289, 293, 313, 349, 353, 361, 373, 379, 409, 419, 421, 433, 439, 443, 463, 499, 509, 523, 571, 577, 599, 601, 607, 613, 619

Offset: 1

Author

Vladimir Shevelev, Aug 30 2013

Keywords

• nonn

Comments

An analog of Labos primes (A080359) on prime powers > 1 (A000961).

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A080459, A186945, A228520, A228592.

Programs

Mathematica

a000961Q[n_]:=(Length[FactorInteger[n]]==1) && IntegerQ[n]; nn=99; t=Table[0,{nn+1}]; s=0; Do[If[a000961Q[k], s++]; If[a000961Q[k/2], s--]; If[s<=nn && t[[s+1]]==0, t[[s+1]]=k], {k, 2, Prime[3*nn]}]; Prepend[Rest[t],2] (* after T. D. Noe's code at A080359 *) (* Peter J. C. Moses, Sep 11 2013 *)

Formula

a(n) <= A186945(n).

Extensions

More terms from Peter J. C. Moses, Aug 30 2013