A309943 Numbers k such that k * d(k) > j * d(j) for all j < k, where d(k) is the number of divisors of k (A000005).

1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 42, 48, 60, 72, 84, 90, 96, 108, 120, 144, 168, 180, 210, 216, 240, 288, 300, 336, 360, 420, 480, 504, 540, 600, 630, 660, 672, 720, 840, 1008, 1080, 1200, 1260, 1440, 1680, 1980, 2016, 2100, 2160, 2520, 3120

Offset: 1

Author

Amiram Eldar, Aug 24 2019

Keywords

• nonn

Comments

Differs from A002093 for n >= 41.

Nicolas asks if there are infinitely many terms of this sequence that are not largely composite (A067128).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..457
• Jean-Louis Nicolas, Nombres hautement composés, Acta Arithmetica, Vol. 49 (1988), pp. 395-412, alternative link. See p. 411.

Crossrefs

Cf. A000005, A002093, A038040, A067128.

Programs

Mathematica

s = {}; dm = 0; Do[d1 = n * DivisorSigma[0, n]; If[d1 > dm, dm = d1; AppendTo[s, n]], {n, 1, 10^4}]; s