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a(n) is the number of divisors of the n-th superabundant number (A004394).
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%I #10 Nov 28 2021 02:55:36

%S 1,2,3,4,6,8,9,10,12,16,18,20,24,30,32,36,40,48,60,72,80,90,96,120,

%T 144,160,180,192,216,224,240,288,320,360,384,432,448,480,576,640,720,

%U 768,864,896,960,1152,1280,1344,1440,1440,1536,1728,1792,1920,2304,2688

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

%C First differs from A002183 at n = 20.

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

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

%H Amiram Eldar, <a href="/A349607/b349607.txt">Table of n, a(n) for n = 1..10000</a>

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

%e a(1) = A000005(A004394(1)) = A000005(1) = 1.

%e a(10) = A000005(A004394(10)) = A000005(120) = 16.

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

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

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 23 2021