A239546 -id:A239546 - cp's OEIS frontend

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

Juri-Stepan Gerasimov, Sep 12 2016

nonn

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, ...

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

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

Subsequence of A131898. Supersequence of A276511.

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

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

\\ 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

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

A384684 Nonprimes k such that sopf(k)^k == sopf(k) (mod k) where sopf = A008472.

Original entry on oeis.org

1, 28, 30, 45, 65, 66, 90, 105, 133, 190, 231, 286, 301, 325, 369, 385, 426, 496, 532, 561, 645, 793, 946, 1016, 1105, 1288, 1353, 1729, 1905, 2041, 2107, 2121, 2275, 2278, 2413, 2465, 2501, 2701, 2737, 2821, 3577, 3781, 3861, 4015, 4123, 4161, 4699

Offset: 1

Juri-Stepan Gerasimov, Jun 06 2025

nonn

Superset of even perfect numbers > 6.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000396, A005835, A008472, A107290, A239546, A302333.

[k: k in [1..5000] | not IsPrime(k) and Modexp(k eq 1 select 0 else &+[p[1]: p in Factorization(k)], k, k) eq (k eq 1 select 0 else &+[p[1]: p in Factorization(k)])];

filter:= proc(k) local s;
  if isprime(k) then return false fi;
  s:= convert(numtheory:-factorset(k),`+`);
  (s &^ k - s) mod k = 0;
end proc:
select(filter, [$1..10000]); # Robert Israel, Jun 12 2025

A008472[n_]:=Sum[p, {p, Select[Divisors[n], PrimeQ]}]; Select[Range[5000],PowerMod[A008472[#],#,#]==A008472[#] &] (* Stefano Spezia, Jun 07 2025 *)

isok(k) = if (!isprime(k), my(s=vecsum(factor(k)[, 1])); Mod(s, k)^k == s); \\ Michel Marcus, Jun 12 2025

cp's OEIS Frontend

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

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