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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

%I #12 Jul 01 2022 10:46:13

%S 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,

%T 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,

%U 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

%N 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.

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

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

%C 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

%H D. W. Wilson, <a href="/A125057/b125057.txt">Table of n, a(n) for n = 1..10000</a>

%t 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 *)

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

%K nonn

%O 1,1

%A _Hugo van der Sanden_, Jan 09 2007

%E Edited by _Robert G. Wilson v_, Jan 11 2007

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)