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

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

Offset

1,1

Comments

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

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

Links

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

Example

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

Prog

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

Crossrefs

Intersection of A000396 and A002191.

Cf. A000203, A146542, A354073, A354074.

Sequence in context: A152953 A066239 A097464 * A166998 A038182 A095723

Adjacent sequences: A354069 A354070 A354071 * A354073 A354074 A354075

Keyword

nonn,changed

Author

Jaroslav Krizek, May 16 2022

Extensions

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

Status

approved