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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.
4
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
1,1
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
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
KEYWORD
nonn
AUTHOR
Hugo van der Sanden, Jan 09 2007
EXTENSIONS
Edited by Robert G. Wilson v, Jan 11 2007
STATUS
approved