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Sum of the divisors of 4^n-1.
11

%I #18 Jan 07 2024 12:27:28

%S 4,24,104,432,1536,8736,22528,111456,473600,1999872,5909760,38054016,

%T 89522176,462274560,2015330304,7304603328,22907191296,166290432000,

%U 366506672128,2220409884672,7645340651520,29833839544320,95821839806976,648494317126656

%N Sum of the divisors of 4^n-1.

%H Max Alekseyev, <a href="/A366603/b366603.txt">Table of n, a(n) for n = 1..1122</a> (terms 1..1062 from Robert Israel)

%F a(n) = sigma(4^n-1) = A000203(A024036(n)).

%F a(n) = A069061(n) * A075708(n). - _Robert Israel_, Nov 22 2023

%e a(4)=432 because 4^4-1 has divisors {1, 3, 5, 15, 17, 51, 85, 255}.

%p a:=n->numtheory[sigma](4^n-1):

%p seq(a(n), n=1..100);

%t DivisorSigma[1,4^Range[30]-1] (* _Paolo Xausa_, Oct 14 2023 *)

%Y Cf. A024036, A000203, A057957, A069061, A075708, A295501, A366602, A366604.

%Y Cf. A075708, A366576, A366613, A366622, A366634, A366653, A366662, A102146, A366684, A366710.

%K nonn

%O 1,1

%A _Sean A. Irvine_, Oct 14 2023