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

1,2

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.

Links

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

Formula

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

Example

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

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

Crossrefs

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

Sequence in context: A303492 A188591 A002183 * A060306 A158614 A303434

Adjacent sequences: A349604 A349605 A349606 * A349608 A349609 A349610

Keyword

nonn

Author

Amiram Eldar, Nov 23 2021

Status

approved