A071541 Number of k's less than or equal to 10^n such that there are middle divisors of k (A071562).

6, 43, 336, 2932, 26870, 252756, 2409731, 23169860, 224059958, 2175865640

Offset

1,1

Links

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

Formula

a(n) = 10^n - A071540(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, A071540, A071562.

Sequence in context: A098665 A153397 A005786 * A146966 A240653 A220097

Adjacent sequences: A071538 A071539 A071540 * A071542 A071543 A071544

Keyword

nonn,hard,more

Author

Robert G. Wilson v, May 31 2002

Extensions

a(8) from Sean A. Irvine, Jul 25 2024

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

Status

approved