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A368651
Numbers k such that 2^sigma(k) - k is a prime.
1
3, 5, 17, 49, 53, 185, 503, 1301, 1689, 1797, 5929, 14747, 20433, 29903, 42137, 64763
OFFSET
1,1
COMMENTS
If it exists, a(17) > 120000. - Michael S. Branicky, Aug 19 2024
EXAMPLE
5 is in the sequence because 2^sigma(5)-5 = 2^6-5 = 59 is prime.
MATHEMATICA
a[n_] := Select[Range@ n, PrimeQ[2^DivisorSigma[1, #] - #] &]; a[20000]
DeleteCases[ParallelTable[If[PrimeQ[2^DivisorSigma[1, k]-k], k, n], {k, 1, 10^4}], n]
PROG
(Magma) [n: n in[1..10000] | IsPrime((2^SumOfDivisors(n)) - n)];
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(16) from J.W.L. (Jan) Eerland, Jan 25 2024
STATUS
approved