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

1,1

Links

Table of n, a(n) for n=1..10.

Formula

a(n) = 10^n - A071541(n). - Amiram Eldar, Jul 27 2024

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}]

Prog

(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

Crossrefs

Cf. A071090, A071541, A071561.

Sequence in context: A353001 A156873 A320977 * A298764 A299562 A299459

Adjacent sequences: A071537 A071538 A071539 * A071541 A071542 A071543

Keyword

nonn,hard,more

Author

Robert G. Wilson v, May 31 2002

Extensions

a(8) from Sean A. Irvine, Jul 24 2024

a(9)-a(10) from Amiram Eldar, Jul 27 2024

Status

approved