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Multiply-perfect numbers that are the sum of the divisors of some number.
3

%I #17 May 12 2024 00:45:23

%S 1,6,28,120,496,672,30240,32760,523776,2178540,23569920,33550336,

%T 45532800,142990848,459818240,1379454720,1476304896,8589869056,

%U 14182439040,31998395520,43861478400,51001180160,66433720320,137438691328,153003540480,403031236608,518666803200

%N Multiply-perfect numbers that are the sum of the divisors of some number.

%C Conjecture: 8128 is only multiply-perfect number that is not in this sequence.

%C The distinct values of A000203(A066961(n)).

%H Amiram Eldar, <a href="/A354073/b354073.txt">Table of n, a(n) for n = 1..50</a>

%e The multiply-perfect number 28 is in the sequence because 28 = sigma(12).

%o (Magma) Set(Sort([&+Divisors(m): m in [1..10^7] | IsIntegral(&+Divisors(&+Divisors(m)) / &+Divisors(m))]))

%Y Intersection of A007691 and A002191.

%Y Cf. A000203, A066961, A354072, A354074.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, May 16 2022

%E a(18)-a(27) from _Amiram Eldar_, May 12 2024