A276493 -id:A276493 - cp's OEIS frontend

A276511 Primes that are equal to the sum of the prime factors of some perfect number.

5, 11, 139, 170141183460469231731687303715884105979

Offset: 1

Juri-Stepan Gerasimov, Sep 06 2016

Primes of the form 2^n + 2*n - 3 such that 2^n - 1 is also prime.
Conjectures (defining x = 170141183460469231731687303715884105727 = A007013(4)):
(1) 2^x + 2*x - 3 is in this sequence;
(2) a(5) = 2^x + 2*x - 3 (see comments of A276493);
(3) primes of A007013 are Mersenne prime exponents A000043, i.e., x is new exponent in A000043.

			a(1) = 5 because 2^2-1 = 3 and 2^2+2*2-3 = 5 are primes,
a(2) = 11 because 2^3-1 = 7 and 2^3+2*3-3 = 11 are primes,
a(3) = 139 because 2^7-1 = 127 and 2^7+2*7-3 = 139 are primes.

Subsequence of A192436.

Cf. A000043, A000396, A000668, A007013, A100118, A276493.

[2^n+2*n-3: n in [1..200] | IsPrime(2^n-1) and IsPrime(2^n+2*n-3)];

A276511:=n->`if`(isprime(2^n-1) and isprime(2^n+2*n-3), 2^n+2*n-3, NULL): seq(A276511(n), n=1..10^3); # Wesley Ivan Hurt, Sep 07 2016

Name suggested by Michel Marcus, Sep 07 2016

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

Original entry on oeis.org

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

cp's OEIS Frontend

A276511 Primes that are equal to the sum of the prime factors of some perfect number.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

Maple

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula