A099641 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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..

LINKS

Table of n, a(n) for n=1..43.

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]

CROSSREFS

Cf. A004648.

Cf. A023143-A023152, A072610.

Sequence in context: A041939 A177714 A273158 * A207189 A285404 A047319

Adjacent sequences: A099638 A099639 A099640 * A099642 A099643 A099644

KEYWORD

nonn

AUTHOR

Labos Elemer, Nov 02 2004

STATUS

approved