A126889 -id:A126889 - cp's OEIS frontend

A126888 a(n) is the smallest positive integer such that floor(a(n)/d(a(n))) = n, or -1 if no such number exists, where d(m) is the number of positive divisors of m.

1, 5, 7, 28, 11, 13, 44, 17, 19, 63, 23, 51, 55, 29, 31, 49, 69, 37, 77, 41, 43, 91, 47, 147, 153, 53, 111, 115, 59, 61, 125, 129, 67, 207, 71, 73, 296, 155, 79, 121, 83, 680, 261, 89, 183, 185, 284, 97, 399, 101, 103, 209, 107, 109, 221, 113, 459, 235, 237, 363, 247, 249

Offset: 1

Leroy Quet, Dec 30 2006

nonn

Hugo van der Sanden and D. W. Wilson, Table of n, a(n) for n = 1..10000

Cf. A000005, A126889, A078709, A125056, A125057.

f[n_] := Block[{k = 1},While[Floor[k/Length[Divisors[k]]] != n, k++ ];k];Table[f[n], {n, 62}] (* Ray Chandler, Jan 04 2007 *)

Extended by Ray Chandler, Jan 04 2007.

Added escape clause to definition at the suggestion of Hugo van der Sanden. - N. J. A. Sloane, Jul 01 2022

A125056 a(n) is the largest positive integer such that floor(a(n)/d(a(n))) = n, where d(m) is the number of positive divisors of m.

Original entry on oeis.org

6, 12, 30, 48, 60, 72, 120, 96, 144, 180, 140, 240, 216, 252, 360, 336, 420, 224, 312, 480, 504, 540, 378, 720, 600, 840, 660, 672, 352, 364, 756, 780, 1080, 960, 1260, 864, 594, 924, 936, 1440, 1320, 1680, 1050, 1056, 1092, 1120, 1512, 1560

Offset: 1

Hugo van der Sanden, Jan 09 2007

nonn

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?

Hugo van der Sanden and D. W. Wilson, Table of n, a(n) for n = 1..10000

Cf. A126888, A000005, A126889, A078709, A125057.

t = Table[ Floor[ n / DivisorSigma[0, n]], {n, 10^5}]; f[n_] := Max@ Flatten@ Position[t, n]; Array[f, 51] (* Robert G. Wilson v, Jan 12 2007 *)

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.

Original entry on oeis.org

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

Hugo van der Sanden, Jan 09 2007

nonn

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

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

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

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 *)

Edited by Robert G. Wilson v, Jan 11 2007

cp's OEIS Frontend

A126888 a(n) is the smallest positive integer such that floor(a(n)/d(a(n))) = n, or -1 if no such number exists, where d(m) is the number of positive divisors of m.

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A125056 a(n) is the largest positive integer such that floor(a(n)/d(a(n))) = n, where d(m) is the number of positive divisors of m.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

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.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions