

A276663


Sum of primes dividing nth perfect number (with repetition).


0



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

Table of n, a(n) for n=1..12.


FORMULA

a(n) = 2^A000043(n) + 2*A000043(n)  3.
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}] (* Requires Mathematica version 10 or later *) (* 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^p1), print1(2^p+2*p3", "))) \\ 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: A197337 A302766 A212199 * A187984 A063626 A154297
Adjacent sequences: A276660 A276661 A276662 * A276664 A276665 A276666


KEYWORD

nonn,easy


AUTHOR

JuriStepan Gerasimov, Sep 12 2016


STATUS

approved



