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.

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

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?

Links

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

Crossrefs

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

Programs

Mathematica

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 *)