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Sum of primes dividing n-th perfect number (with repetition).
1

%I #36 Oct 21 2024 04:36:29

%S 5,11,39,139,8215,131103,524323,2147483707,2305843009213694071,

%T 618970019642690137449562287,162259276829213363391578010288339,

%U 170141183460469231731687303715884105979

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

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

%C The next term is too large to include.

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

%H Amiram Eldar, <a href="/A276663/b276663.txt">Table of n, a(n) for n = 1..18</a>

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

%F a(n) = A001414(A000396(n)). - _Michel Marcus_, Sep 18 2016

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

%t Table[Total[Times@@@FactorInteger[PerfectNumber[n]]],{n,15}] (* _Harvey P. Dale_, Sep 22 2019 *)

%o (PARI) \\ Ochem & Rao: no odd perfect numbers below 10^1500

%o forprime(p=2,2281, if(ispseudoprime(t=2^p-1), print1(2^p+2*p-3", "))) \\ _Charles R Greathouse IV_, Sep 18 2016

%Y Subsequence of A131898. Supersequence of A276511.

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

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Sep 12 2016