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

Author

Labos Elemer, Jan 09 2002

Keywords

• nonn

Comments

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

Links

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

Crossrefs

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

Programs

Mathematica

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]