A276663 Sum of primes dividing n-th perfect number (with repetition).

5, 11, 39, 139, 8215, 131103, 524323, 2147483707, 2305843009213694071, 618970019642690137449562287, 162259276829213363391578010288339, 170141183460469231731687303715884105979

Offset

1,1

Comments

Numbers that are equal to the sum of the prime factors (A001414) of some perfect number.

The next term is too large to include.

A001222(a(n)) is 1, 1, 2, 1, 3, 4, 2, 2, 4, 6, 7, 1, 11, ...

Links

Amiram Eldar, Table of n, a(n) for n = 1..18

Formula

a(n) = 2^A000043(n) + 2*A000043(n) - 3, assuming that there are no odd perfect numbers.

a(n) = A001414(A000396(n)). - Michel Marcus, Sep 18 2016

Example

39 is in this sequence because 39 - 2^(5 - 1) = 31 = 2^5 - 1 and 31 is prime.

Mathematica

Table[Total[Times@@@FactorInteger[PerfectNumber[n]]], {n, 15}] (* Harvey P. Dale, Sep 22 2019 *)

Prog

(PARI) \\ Ochem & Rao: no odd perfect numbers below 10^1500
forprime(p=2, 2281, if(ispseudoprime(t=2^p-1), print1(2^p+2*p-3", "))) \\ Charles R Greathouse IV, Sep 18 2016

Crossrefs

Subsequence of A131898. Supersequence of A276511.

Cf. A000043, A000396, A001222, A001414, A007013, A192436, A239546, A276493.

Sequence in context: A302766 A369982 A212199 * A187984 A063626 A154297

Adjacent sequences: A276660 A276661 A276662 * A276664 A276665 A276666

Keyword

nonn

Author

Juri-Stepan Gerasimov, Sep 12 2016

Status

approved