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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.
0
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
1,2
COMMENTS
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.
EXAMPLE
Q(29) = 18 and Q(29) - 6*29/Pi^2 = 0.37011... is smaller than Q(1) - 6/Pi^2 = 0.39207...
MATHEMATICA
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 *)
PROG
(PARI) 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
CROSSREFS
Cf. A005117, A275390 (indices of records of |Q(m)-6*m/Pi^2|).
Sequence in context: A044462 A161714 A049743 * A033915 A192358 A123848
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Jinyuan Wang, Jan 16 2021
STATUS
approved