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

1,2

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. 196-201.

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: A137604 A034901 A343149 * A109976 A011768 A052487

Adjacent sequences: A275387 A275388 A275389 * A275391 A275392 A275393

Keyword

nonn

Author

Charles R Greathouse IV, Aug 07 2016

Status

approved