A071540 Number of k's less than or equal to 10^n such that there are no middle divisors of k (A071561).
4, 57, 664, 7068, 73130, 747244, 7590269, 76830140, 775940042, 7824134360
Offset: 1
Programs
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Mathematica
f[n_] := Plus @@ Select[ Divisors[n], Sqrt[n/2] <= # < Sqrt[n*2] &]; s = 0; k = 0; Do[ While[k < 10^n, k++; If[ f[k] == 0, s++ ]]; Print[s], {n, 1, 7}] -
PARI
lista(nmax) = {my(c = 0, pow = 10); for(k = 1, 10^nmax, if(sumdiv(k, d, if(d^2 >= k/2 && d^2 < 2*k, d, 0)) == 0, c++); if(k == pow, print1(c, ", "); pow *= 10));} \\ Amiram Eldar, Jul 27 2024
Formula
a(n) = 10^n - A071541(n). - Amiram Eldar, Jul 27 2024
Extensions
a(8) from Sean A. Irvine, Jul 24 2024
a(9)-a(10) from Amiram Eldar, Jul 27 2024