A349607 a(n) is the number of divisors of the n-th superabundant number (A004394).

1, 2, 3, 4, 6, 8, 9, 10, 12, 16, 18, 20, 24, 30, 32, 36, 40, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 192, 216, 224, 240, 288, 320, 360, 384, 432, 448, 480, 576, 640, 720, 768, 864, 896, 960, 1152, 1280, 1344, 1440, 1440, 1536, 1728, 1792, 1920, 2304, 2688

Offset: 1

Author

Amiram Eldar, Nov 23 2021

Keywords

• nonn

Comments

First differs from A002183 at n = 20.

The first position n where a(n+1) = a(n) is n = 49: a(49) = a(50) = 1440.

The first position n where a(n+1) < a(n) is n = 173: a(173) = 5308416 and a(174) = 5160960.

Examples

			a(1) = A000005(A004394(1)) = A000005(1) = 1.
a(10) = A000005(A004394(10)) = A000005(120) = 16.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A002183, A004394, A007626, A349608.

Programs

Mathematica

s = {}; rm = 0; Do[r = DivisorSigma[1, n]/n; If[r > rm, rm = r; AppendTo[s, DivisorSigma[0, n]]], {n, 1, 10^5}]; s

Formula

a(n) = A000005(A004394(n)).