A073162
n is such that partial sum of pi(k) from 1 to n is divisible by n.
Original entry on oeis.org
1, 3, 17, 37, 9107, 156335, 679083, 1068131, 4883039, 101691357
Offset: 1
a(3) = 17 because 0+1+2+2+3+3+4+4+4+4+5+5+6+6+6+6+7 = 68 = 4*17.
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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 *)
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
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.
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s = 0; Do[s = s + PrimePi[n]; If[ IntegerQ[s/n], Print[{n, s, s/n}]], {n, 1, 10^8}]
Original entry on oeis.org
0, 1, 4, 7, 604, 7552, 28720, 43501, 176868, 3016559
Offset: 1
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, Sum(17)/17 = 4 = a(3).
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s = 0; Do[s = s + PrimePi[n]; If[ IntegerQ[s/n], Print[{n, s, s/n}]], {n, 1, 10^8}]
A072111
Partial sum of pi(k) from k = 1 to 2^n.
Original entry on oeis.org
1, 5, 19, 61, 203, 669, 2279, 7797, 27213, 96111, 343965, 1240617, 4513763, 16546859, 61027965, 226454967, 844181631, 3161518957, 11886015725, 44847272299, 169747439789, 644345294711, 2452231140853, 9354606971985
Offset: 1
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s = 0; k = 1; Do[ While [k <= 2^n, s = s + PrimePi[k]; k++ ]; Print[s], {n, 1, 28} ]
Showing 1-4 of 4 results.
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