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, 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

Offset: 1

Author

Charles R Greathouse IV, Aug 07 2016

Keywords

• nonn

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. 196-201.

Crossrefs

Cf. A005117, A013928.

Programs

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", ")))