login
A276663
Sum of primes dividing n-th perfect number (with repetition).
1
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
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.
Sequence in context: A302766 A369982 A212199 * A187984 A063626 A154297
KEYWORD
nonn
AUTHOR
STATUS
approved