A133033 -id:A133033 - cp's OEIS frontend

A154896 Sum of proper divisors minus the number of proper divisors of the perfect number A000396(n).

3, 23, 487, 8115, 33550311, 8589869023, 137438691291, 2305843008139952067, 2658455991569831744654692615953842055, 191561942608236107294793378084303638130997321548169039

Offset: 1

Omar E. Pol, Jan 25 2009

nonn

a(n) is also the difference between the n-th perfect number and its number of proper divisors.

			a(2) is 23 because the second perfect number is 28 and the sum of proper divisors of 28 is also 28 = 1+2+4+7+14 and the number of proper divisors of 28 is 5, then 28-5 = 23.

Cf. A000396, A001065, A032741, A133033, A152770.

a(n) = A152770(A000396(n)) = A000396(n)-A133033(n).

More terms from Max Alekseyev, Dec 12 2011

A154895 Perfect numbers whose number of proper divisors is prime.

Original entry on oeis.org

6, 28, 8128, 137438691328, 2305843008139952128

Offset: 1

Omar E. Pol, Jan 25 2009

nonn

The next term is too large to include in the data section. If there are no odd perfect numbers then the next term is a(6) = 2^606 * (2^607 - 1) = 1.410... * 10^365. - Amiram Eldar, Jul 29 2020

			28 is member because the number of proper divisors of 28 is 5, a prime number.

Cf. A000396, A006516, A032741, A133033, A154896, A172461.

Table[2^(p-1)*(2^p-1), {p, Select[MersennePrimeExponent[Range[8]], PrimeQ[2# - 1] &]}] (* Amiram Eldar, Jul 29 2020 *)

a(n) = A006516(A172461(n)), assuming that odd perfect numbers do not exist. - Amiram Eldar, Jul 29 2020

cp's OEIS Frontend

A154896 Sum of proper divisors minus the number of proper divisors of the perfect number A000396(n).

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