A075033 Numbers n such that tau(n) <= tau(n+1) <= tau(n+2) <= tau(n+3) where tau(n) = number of divisors of n.

1, 13, 25, 33, 37, 61, 73, 85, 93, 97, 121, 133, 141, 145, 157, 187, 193, 201, 205, 213, 217, 229, 241, 242, 243, 253, 277, 283, 301, 361, 373, 393, 397, 421, 427, 445, 453, 457, 481, 537, 541, 547, 603, 613, 633, 661, 662, 663, 697, 723, 733, 745, 757, 781

Offset: 1

Author

Amarnath Murthy, Sep 02 2002

Keywords

• nonn

Links

• Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A075032, A075034, A075035.

Programs

Mathematica

With[{s = Partition[Differences@ Array[DivisorSigma[0, #] &, 800], 3, 1]}, Position[s, ?(AllTrue[#, # >= 0 &] &), {1}, Heads -> False][[All, 1]]] (* _Michael De Vlieger, Jun 28 2020 *)

Python

from sympy import divisor_count as tau
[n for n in range(1, 801) if tau(n) <= tau(n+1) <= tau(n+2) <= tau(n+3)] # Karl V. Keller, Jr., Jul 10 2020

Extensions

Added missing term and a(11)-a(54) from Donovan Johnson, Jun 15 2009