

A275390


Numbers n for which n/zeta(2)  Q(n) sets a new record, where Q(x) is the number of squarefree numbers up to x.


1



1, 2, 3, 6, 7, 15, 23, 39, 42, 43, 115, 223, 231, 239, 474, 719, 1367, 1403, 1406, 1407, 1410, 1411, 1419, 1646, 1659, 1662, 1663, 3423, 8810, 8818, 8819, 8822, 8823, 8915, 9239, 9242
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Assuming the Riemann hypothesis, Vaidya proved that Q(n) = 6*n/Pi^2 + O(n^k) for any k > 2/5.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
A. M. Vaidya, On the order of the error function of the square free numbers, Proc. Nat. Inst. Sci. India Part A 32 (1966), pp. 196201.


PROG

(PARI) ct=r=0; for(n=1, 1e4, if(issquarefree(n), ct++); t=abs(n/zeta(2)ct); if(t>r, r=t; print1(n", ")))


CROSSREFS

Cf. A005117, A013928.
Sequence in context: A125167 A137604 A034901 * A109976 A011768 A052487
Adjacent sequences: A275387 A275388 A275389 * A275391 A275392 A275393


KEYWORD

nonn


AUTHOR

Charles R Greathouse IV, Aug 07 2016


STATUS

approved



