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Number of k's less than or equal to 10^n such that there are no middle divisors of k (A071561).
6

%I #12 Jul 27 2024 09:41:41

%S 4,57,664,7068,73130,747244,7590269,76830140,775940042,7824134360

%N Number of k's less than or equal to 10^n such that there are no middle divisors of k (A071561).

%F a(n) = 10^n - A071541(n). - _Amiram Eldar_, Jul 27 2024

%t 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}]

%o (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

%Y Cf. A071090, A071541, A071561.

%K nonn,hard,more

%O 1,1

%A _Robert G. Wilson v_, May 31 2002

%E a(8) from _Sean A. Irvine_, Jul 24 2024

%E a(9)-a(10) from _Amiram Eldar_, Jul 27 2024