A073164 -id:A073164 - cp's OEIS frontend

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

Labos Elemer, Jul 18 2002

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

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

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

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

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 *)

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

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

a(10) from Donovan Johnson, Dec 15 2009

A073163 Partial sums of Pi(k) arising in A073162.

Original entry on oeis.org

0, 3, 68, 259, 5500628, 1180641920, 19503263760, 46464766631, 863653341852, 306757978180563

Offset: 1

Labos Elemer, Jul 18 2002

			Sum of first 17 values of Pi(n) equals 0+1+2+2+3+3+4+4+4+4+5+5+6+6+6+6+7 = 68 = 4*17. To continue, see A073224.

Cf. A046992, A000720, A073162, A073164 & A073224.

s = 0; Do[s = s + PrimePi[n]; If[ IntegerQ[s/n], Print[{n, s, s/n}]], {n, 1, 10^8}]

Values of s(n) = A046992(n) such that s(n)/n is an integer.

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

a(10) from Donovan Johnson, Dec 15 2009

cp's OEIS Frontend

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

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