A056758 -id:A056758 - cp's OEIS frontend

A067023 Sigma-crowded numbers: n such that d(n)/sigma(n) is larger than d(m)/sigma(m) for all m > n.

1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 42, 48, 60, 72, 80, 84, 90, 96, 120, 126, 144, 168, 180, 210, 240, 252, 280, 288, 300, 360, 420, 432, 480, 504, 540, 560, 600, 630, 720, 840, 900, 1008, 1080, 1260

Offset: 1

Labos Elemer, Jan 09 2002

nonn

Since d(m) < 2*sqrt(m) < 2*sigma(m), we need only test values of m < (2*sigma(n)/d(n))^2.

Donovan Johnson, Table of n, a(n) for n = 1..300

An analog of A066523. Cf. A002182, A000005, A000203, A004394, A034884, A056758.

crowded[n_] := Module[{}, stop=(2/(dovern=DivisorSigma[0, n]/DivisorSigma[1, n]))^2; For[m=n+1, m=dovern, Return[False]]]; True]; Select[Range[1, 13000], crowded]

A374793 a(n) is the largest k such that tau(k)^n >= k.

Original entry on oeis.org

2, 1260, 27935107200, 29564884570506808579056000

Offset: 1

Jon E. Schoenfield, Jul 20 2024

Let prime(j)# denote the product of the first j primes, A002110(j); then
  a(1)  = prime(1)# = 2,
  a(2)  = 6*prime(4)# = 1260,
  a(3)  = 2880*prime(8)# = 2.7935...*10^10,
  a(4)  = 907200*prime(16)# = 2.9564...*10^25,
  a(5) >= 259459200*prime(30)# = 8.2015...*10^54,
  a(6) >= 3238237626624000*prime(52)# = 3.4403...*10^111,
  a(7) >= 248818180782850398720000*prime(91)# = 5.4351...*10^218.

			27935107200 = 2^7 * 3^3 * 5^2 * 7^1 * 11^1 * 13^1 * 17^1 * 19^1,
so tau(27935107200) = (7+1)*(3+1)*(2+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1) = 8*4*3*2*2*2*2*2 = 3072; 3072^3 = 28991029248 > 27935107200, and there is no larger number k such that tau(k)^3 >= k, so a(3) = 27935107200.

Cf. A000005, A035033, A056757, A056758.

cp's OEIS Frontend

A067023 Sigma-crowded numbers: n such that d(n)/sigma(n) is larger than d(m)/sigma(m) for all m > n.

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