A354074 -id:A354074 - cp's OEIS frontend

A354072 Perfect numbers that are the sum of the divisors of some number.

6, 28, 496, 33550336, 8589869056, 137438691328, 2305843008139952128, 2658455991569831744654692615953842176, 191561942608236107294793378084303638130997321548169216, 13164036458569648337239753460458722910223472318386943117783728128

Offset: 1

Jaroslav Krizek, May 16 2022

nonn

The distinct values of A000203(A146542(n)).

Conjecture: 8128 is the only perfect number that is not in this sequence.

			The perfect number 28 is in the sequence because 28 = sigma(12).
sigma(727145809044307968) = sigma(1152771972099211264) = 2305843008139952128.

Amiram Eldar, Table of n, a(n) for n = 1..11

Intersection of A000396 and A002191.

Cf. A000203, A146542, A354073, A354074.

Set(Sort([&+Divisors(m): m in [1..10^7] | &+Divisors(&+Divisors(m)) eq 2 * &+Divisors(m)]))

a(8)-a(10) from Amiram Eldar, May 12 2024

A354073 Multiply-perfect numbers that are the sum of the divisors of some number.

Original entry on oeis.org

1, 6, 28, 120, 496, 672, 30240, 32760, 523776, 2178540, 23569920, 33550336, 45532800, 142990848, 459818240, 1379454720, 1476304896, 8589869056, 14182439040, 31998395520, 43861478400, 51001180160, 66433720320, 137438691328, 153003540480, 403031236608, 518666803200

Offset: 1

Jaroslav Krizek, May 16 2022

nonn

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

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

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

Amiram Eldar, Table of n, a(n) for n = 1..50

Intersection of A007691 and A002191.

Cf. A000203, A066961, A354072, A354074.

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

a(18)-a(27) from Amiram Eldar, May 12 2024

cp's OEIS Frontend

A354072 Perfect numbers that are the sum of the divisors of some number.

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