A075034 -id:A075034 - cp's OEIS frontend

A075032 Numbers n such that tau(n) <= tau(n+1) <= tau(n+2) where tau(n) = number of divisors of n.

1, 2, 13, 14, 25, 26, 33, 34, 37, 38, 43, 61, 62, 73, 74, 85, 86, 93, 94, 97, 98, 103, 115, 118, 121, 122, 133, 134, 141, 142, 145, 146, 157, 158, 163, 187, 188, 193, 194, 201, 202, 205, 206, 213, 214, 217, 218, 229, 230, 241, 242, 243, 244, 253, 254, 274, 277

Offset: 1

Amarnath Murthy, Sep 02 2002

nonn

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

Cf. A000005, A075033, A075034, A075035, A005238 (subsequence).

from sympy import divisor_count as tau
[n for n in range(1,303) if tau(n) <= tau(n+1) <= tau(n+2)] # Karl V. Keller, Jr., Jul 10 2020

Corrected and extended by Benoit Cloitre, Sep 07 2002

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

Original entry on oeis.org

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

Amarnath Murthy, Sep 02 2002

nonn

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

Cf. A000005, A075032, A075034, A075035.

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 *)

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

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

A075035 Numbers n such that tau(n) >= tau(n+1) >= tau(n+2) >= tau(n+3) where tau(n) = number of divisors of n.

Original entry on oeis.org

20, 32, 44, 56, 80, 84, 92, 104, 116, 140, 170, 176, 200, 212, 216, 224, 230, 242, 260, 296, 300, 324, 332, 344, 374, 380, 392, 434, 440, 444, 464, 476, 500, 506, 512, 560, 594, 602, 608, 620, 632, 644, 650, 696, 704, 714, 715, 716, 740, 776, 800, 804, 836

Offset: 1

Amarnath Murthy, Sep 02 2002

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Cf. A075032, A075033, A075034.

Position[Partition[DivisorSigma[0,Range[900]],4,1],?(Max[ Differences[ #]]< 1&),1,Heads->False]//Flatten (* _Harvey P. Dale, Sep 05 2019 *)

from sympy import divisor_count as tau
[n for n in range(1,901) if tau(n) >= tau(n+1) >= tau(n+2) >= tau(n+3)] # Karl V. Keller, Jr., Jul 10 2020

More terms from Benoit Cloitre, Sep 07 2002

cp's OEIS Frontend

A075032 Numbers n such that tau(n) <= tau(n+1) <= tau(n+2) where tau(n) = number of divisors of n.

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

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A075035 Numbers n such that tau(n) >= tau(n+1) >= tau(n+2) >= tau(n+3) where tau(n) = number of divisors of n.

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