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A231627
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Numbers n such that sigma(sigma(n)) - sigma(n) - 1 is prime.
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1
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3, 5, 20, 24, 26, 29, 38, 41, 44, 45, 54, 56, 59, 60, 65, 78, 80, 81, 83, 87, 90, 92, 95, 101, 102, 108, 110, 114, 120, 122, 123, 135, 136, 137, 142, 143, 146, 147, 150, 153, 158, 159, 164, 167, 168, 174, 176, 177, 178, 180, 184, 185, 187, 190, 194, 197, 203, 209
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(4)= 24: sigma(sigma(n))-sigma(n)-1= 168-60-1= 107, which is prime.
a(10)= 45: sigma(sigma(n))-sigma(n)-1= 168-78-1= 89, which is prime.
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MAPLE
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with(numtheory): KD := proc() local a; a:= sigma(sigma(n))-sigma(n)-1; if isprime(a) then RETURN (n); fi; end: seq(KD(), n=1..500);
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MATHEMATICA
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Select[Range[300], PrimeQ[DivisorSigma[1, DivisorSigma[1, #]]-DivisorSigma[ 1, #]-1]&] (* Harvey P. Dale, Jun 04 2021 *)
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CROSSREFS
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Cf. A051027 (a(n): sigma(sigma(n)).
Cf. A228567 (primes: sigma(sigma(n))-sigma(n)).
Cf. A231587 (numbers n: sigma(sigma(n))-sigma(n)+1 is prime).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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