A125057 a(n) is the number of positive integers m such that floor(m/d(m)) = n, where d(m) is the number of positive divisors of m.

5, 4, 9, 3, 7, 5, 6, 11, 7, 4, 8, 6, 9, 5, 4, 16, 7, 4, 8, 7, 11, 5, 10, 7, 7, 8, 7, 12, 9, 6, 10, 8, 8, 8, 10, 6, 4, 7, 7, 15, 8, 4, 11, 11, 8, 12, 7, 11, 7, 9, 8, 8, 12, 14, 8, 12, 8, 8, 11, 5, 14, 7, 7, 9, 5, 8, 4, 13, 7, 8, 12, 10, 6, 9, 14, 11, 9, 8, 9, 12, 13, 8, 8, 9, 9, 10, 7, 11, 14, 3, 10

Offset: 1

Author

Hugo van der Sanden, Jan 09 2007

Keywords

• nonn

Comments

We know the sequence is well-defined given the limit x/d(x) > 0.5*sqrt(x) from comments in A036763.

Does every positive integer n equal floor(m/d(m)) for some m?

First occurrence of k>2: 4, 2, 1, 7,5 , 11, 3, 23, 8, 28, 68, 54, 40, 16, 251, 572, 141, ???, ???, ???, 529, ..., (630). - Robert G. Wilson v, Jan 11 2007

Links

• D. W. Wilson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A126888, A000005, A126889, A078709, A125056.

Programs

Mathematica

t = Table[Floor[n/DivisorSigma[0, n]], {n, 10^5}]; f[n_] := Length@Select[t, # == n &]; Array[f, 91] (* Robert G. Wilson v, Jan 11 2007 *)

Extensions

Edited by Robert G. Wilson v, Jan 11 2007