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A189373
Perfect numbers k such that k+1 is prime.
0
6, 28, 33550336, 137438691328
OFFSET
1,1
COMMENTS
Joerg Arndt checked that up to exponent r=110503 of the corresponding Mersenne prime 2^r - 1 the number n=2^(r-1)*(2^r -1) is not pseudoprime.
The listed perfect numbers have exponents r in 2,3,13,19.
FORMULA
a(n) = A061644(n) - 1. - Amiram Eldar, May 06 2024
EXAMPLE
We have a(3) = 33550336 since 33550337 is prime and there is no other such perfect number less than a(3) and that exceeds a(2) = 28.
PROG
(PARI)
{e=[2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787]; } /* exponents of Mersenne primes */
for(n=1, #e, p=(2^e[n]-1)*(2^(e[n]-1)); if(ispseudoprime(p+1), print1(p, ", ")));
CROSSREFS
KEYWORD
nonn,bref,hard,more
AUTHOR
Luis H. Gallardo, Apr 23 2011
STATUS
approved