Sign of A062778

[Berny]

franktaw at netscape.net dice:

> Sequence A062778 (Mobius transform of prime pi function) has the nonn 
> keyword, and it certainly seems to be entirely non-negative (I checked 
> up to 2400; after 210, the minimum value is 8).  However, it isn't 
> entirely obvious.  Can anybody prove it?

After extending the search up to 10000, it also seems that for the 
following pairs there are no a(n)<=t(k) for all n>k:

t(k) k
0    10
1    15
2    60
4    96
5    210
8    330
11   420
12   570
17   600
19   630
24   840
25   870
27   990
31   1050
34   1260
35   1320
36   1470
44   1560
48   1590
50   1890
52   2310
59   2520
67   2640
69   3360
76   3570
93   3780
94   4620
103  4830
108  5460
121  5610
124  5670
132  6090
145  6510
146  6930
147  8190
162  8580
172  8610
181  9240

A lot of new sequences arise!

                Berny Boncompagni

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