A075032 -id:A075032 - cp's OEIS frontend

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

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

A075034 Numbers n such that tau(n) >= tau(n+1) >= tau(n+2) where tau(n) = number of divisors of n.

Original entry on oeis.org

20, 21, 32, 33, 44, 45, 56, 57, 75, 80, 81, 84, 85, 92, 93, 104, 105, 116, 117, 132, 135, 140, 141, 144, 147, 165, 170, 171, 176, 177, 189, 200, 201, 204, 212, 213, 216, 217, 224, 225, 230, 231, 242, 243, 252, 260, 261, 272, 285, 296, 297, 300, 301, 315, 324

Offset: 1

Amarnath Murthy, Sep 02 2002

nonn

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

Cf. A000005 (tau), A075032, A075033, A075035.

nn = 400; t = DivisorSigma[0, Range[nn]]; Select[Range[nn-2], t[[#]] >= t[[#+1]] >= t[[#+2]] &] (* Harvey P. Dale, May 24 2012 *)

from sympy import divisor_count as tau
[n for n in range(1,333) if tau(n) >= tau(n+1) >= tau(n+2)] # Karl V. Keller, Jr., Jul 10 2020

More terms from Benoit Cloitre, Sep 07 2002

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

A359125 Largest prime factor of A359124(n).

Original entry on oeis.org

2, 13, 31, 19, 6173, 123457, 154321, 333667, 333667, 3388877, 4281283, 2630197, 26798700427, 8663199947, 2523244037, 12873492085621702963, 32929947197382727, 17539959825403, 71595329159622797, 325339942922532262019, 9999103057380477280607, 17465868005034957301, 1423364280511

Offset: 1

N. J. A. Sloane, Dec 20 2022

Has the same relation to A359124 as A075032 does to A007908. Suggested by A069048.

Cf. A007908, A069048, A075032, A359124.

FactorInteger[#][[-1,1]]&/@Table[FromDigits[Flatten[IntegerDigits/@Range[n]]]+1,{n,30}] (* Harvey P. Dale, Dec 20 2022 *)

from sympy import factorint
def a(n): return max(factorint(int("".join(map(str, range(1, n+1)))) + 1))
print([a(n) for n in range(1, 24)]) # Michael S. Branicky, Dec 20 2022

cp's OEIS Frontend

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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A075034 Numbers n such that tau(n) >= tau(n+1) >= tau(n+2) 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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A359125 Largest prime factor of A359124(n).

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