A125057 - OEIS

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

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OFFSET

1,1

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

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 *)

CROSSREFS

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

Sequence in context: A241420 A077142 A156057 * A021186 A195705 A212878

Adjacent sequences: A125054 A125055 A125056 * A125058 A125059 A125060

KEYWORD

nonn

AUTHOR

Hugo van der Sanden, Jan 09 2007

EXTENSIONS

Edited by Robert G. Wilson v, Jan 11 2007

STATUS

approved