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User: Adedoyin M. Adegbuyi

Adedoyin M. Adegbuyi has authored 1 sequences.

A339865 Squarefree numbers k for which Q(k) - 6*k/Pi^2 sets a new record minimum, where Q(x) is the number of squarefree numbers up to x.

1, 29, 57, 173, 177, 365, 370, 377, 379, 381, 1090, 1865, 5578, 5590, 11326, 11333, 11863, 11865, 11877, 11882, 12657, 13881, 32285, 32313, 32833, 32853, 32881, 33034, 33041, 37558, 37561, 37571, 37573, 37577, 37689, 38729, 38858, 38863, 38865, 38873, 38877

Offset: 1

Adedoyin M. Adegbuyi, Jan 15 2021

nonn

The sequence contains each squarefree integer k where Q(k) - 6*k/Pi^2 is smaller than Q(m) - 6*m/Pi^2 for any 0 < m < k. Where both m and k are squarefree. It is well known that Q(k) is asymptotic to 6*k/Pi^2.

			Q(29) = 18 and Q(29) - 6*29/Pi^2 = 0.37011... is smaller than Q(1) - 6/Pi^2 = 0.39207...

Cf. A005117, A275390 (indices of records of |Q(m)-6*m/Pi^2|).

s = Select[Range[50000], SquareFreeQ]; d = 6*s/Pi^2 - Range[Length[s]]; s[[Flatten[Position[d, #][[1]] & /@ Union @ FoldList[Max, d]]]] (* Amiram Eldar, Jan 27 2021 *)

lista(nn) = {my(m=oo, nb=0, x); forsquarefree(n=1, nn, nb++; x = nb - 6*n[1]/Pi^2; if (x < m, m = x; print1(n[1], ", ")););} \\ Michel Marcus, Jan 26 2021

More terms from Jinyuan Wang, Jan 16 2021

cp's OEIS Frontend

User: Adedoyin M. Adegbuyi

A339865 Squarefree numbers k for which Q(k) - 6*k/Pi^2 sets a new record minimum, where Q(x) is the number of squarefree numbers up to x.

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