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%I #21 May 12 2024 00:45:45
%S 6,28,496,33550336,8589869056,137438691328,2305843008139952128,
%T 2658455991569831744654692615953842176,
%U 191561942608236107294793378084303638130997321548169216,13164036458569648337239753460458722910223472318386943117783728128
%N Perfect numbers that are the sum of the divisors of some number.
%C The distinct values of A000203(A146542(n)).
%C Conjecture: 8128 is the only perfect number that is not in this sequence.
%H Amiram Eldar, <a href="/A354072/b354072.txt">Table of n, a(n) for n = 1..11</a>
%e The perfect number 28 is in the sequence because 28 = sigma(12).
%e sigma(727145809044307968) = sigma(1152771972099211264) = 2305843008139952128.
%o (Magma) Set(Sort([&+Divisors(m): m in [1..10^7] | &+Divisors(&+Divisors(m)) eq 2 * &+Divisors(m)]))
%Y Intersection of A000396 and A002191.
%Y Cf. A000203, A146542, A354073, A354074.
%K nonn
%O 1,1
%A _Jaroslav Krizek_, May 16 2022
%E a(8)-a(10) from _Amiram Eldar_, May 12 2024
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