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Corresponding values of primes p from A247821 and A247838.
6

%I #20 Sep 08 2022 08:46:09

%S 7,8191,8191,131071,524287,524287,2147483647,2147483647,

%T 2305843009213693951,2305843009213693951,2305843009213693951,

%U 2305843009213693951

%N Corresponding values of primes p from A247821 and A247838.

%C Conjecture: all terms are Mersenne primes (A000668).

%C Conjecture: next terms are 2305843009213693951, 2305843009213693951, 2305843009213693951, 2305843009213693951 and 618970019642690137449562111. - _Jaroslav Krizek_, Mar 25 2015

%F a(n) = sigma(sigma(2*A247821(n)-1)) = A000203(A000203(2*A247821(n)-1)) = A051027(2*A247821(n)-1).

%F a(n) = sigma(sigma(A247838(n))) = A000203(A000203(A247838(n))) = A051027(A247838(n)) .

%e a(2) = 8191 because sigma(sigma(2*A247821(2)-1)) = sigma(sigma(A247838(2))) = 8191.

%o (Magma) [SumOfDivisors(SumOfDivisors(n)): n in [A247838(n)]

%Y Cf. A000203, A008438, A247790, A247791, A247820, A247821, A247823, A247954.

%K nonn,more

%O 1,1

%A _Jaroslav Krizek_, Sep 28 2014

%E a(7)-a(8) from _Jaroslav Krizek_, Mar 25 2015

%E a(9)-a(12) from _Giovanni Resta_, Feb 14 2020