A099641 Number of solutions to x*frac[p(x)/x]<=Log[n] or A004648(n)<=Log[n].

1, 5, 6, 12, 13, 14, 15, 31, 32, 34, 69, 73, 74, 75, 76, 77, 181, 445, 1052, 6455, 6456, 6457, 6459, 6460, 6466, 15928, 16055, 40073, 40078, 40080, 40081, 40082, 40083, 40122, 100362, 100364, 100365, 251707, 251711, 251712, 251717, 251719, 251721

Offset: 1

Author

Labos Elemer, Nov 02 2004

Keywords

• nonn

Comments

Solutions appear in clusters because of features of diagram visible at A004648. Later clusters are introduced by 6455, 15928, 40073, 100362, 251707, 637235, 4124455, respectively.

Number of solutions in consecutive clusters seem to be as follows: 1,2,4,3,6,1,1,1,6,2,7,3 etc..

Crossrefs

Cf. A004648.

Cf. A023143-A023152, A072610.

Programs

Mathematica

ta={{0}};Do[s=w*fra[Prime[w]/w];If[ !Greater[s, Log[n]], Print[w]; ta=Append[ta, w]], {w, 1, 1000000}];ta=Delete[ta, 1]