A073162 n is such that partial sum of pi(k) from 1 to n is divisible by n.

1, 3, 17, 37, 9107, 156335, 679083, 1068131, 4883039, 101691357

Offset: 1

Author

Labos Elemer, Jul 18 2002

Keywords

• nonn
• more

Comments

a(11) > 10^12. - Donovan Johnson, Mar 19 2011

a(11) > 10^13. - Lucas A. Brown, Oct 05 2020

Examples

			a(3) = 17 because 0+1+2+2+3+3+4+4+4+4+5+5+6+6+6+6+7 = 68 = 4*17.
		

Crossrefs

Cf. A046992, A000720, A073163, A073164, A073224.

Programs

Mathematica

s = 0; Do[s = s + PrimePi[n]; If[ IntegerQ[s/n], Print[{n, s, s/n}]], {n, 1, 10^8}]
Module[{nn=11 10^5,pspi},pspi=Accumulate[PrimePi[Range[nn]]];Select[Thread[{Range[nn],pspi}],Mod[#[[2]],#[[1]]]==0&]][[;;,1]] (* The program generates the first 8 terms of the siequence. *) (* Harvey P. Dale, Mar 19 2025 *)

Formula

Solutions to Mod[A046992(x), x]=0

Extensions

Edited and extended by Robert G. Wilson v, Jul 20 2002

a(10) from Donovan Johnson, Dec 15 2009