A231627 - OEIS

%I #10 Nov 04 2024 02:29:59

%S 3,5,20,24,26,29,38,41,44,45,54,56,59,60,65,78,80,81,83,87,90,92,95,

%T 101,102,108,110,114,120,122,123,135,136,137,142,143,146,147,150,153,

%U 158,159,164,167,168,174,176,177,178,180,184,185,187,190,194,197,203,209

%N Numbers k such that sigma(sigma(k)) - sigma(k) - 1 is prime.

%H K. D. Bajpai, <a href="/A231627/b231627.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 24: sigma(sigma(n))-sigma(n)-1 = 168-60-1 = 107, which is prime.

%e a(10) = 45: sigma(sigma(n))-sigma(n)-1 = 168-78-1 = 89, which is prime.

%p 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);

%t Select[Range[300],PrimeQ[DivisorSigma[1,DivisorSigma[1,#]]-DivisorSigma[ 1,#]-1]&] (* _Harvey P. Dale_, Jun 04 2021 *)

%Y Cf. A000203 (a(n): sigma(n)).

%Y Cf. A051027 (a(n): sigma(sigma(n))).

%Y Cf. A228567 (primes: sigma(sigma(n))-sigma(n)).

%Y Cf. A231587 (numbers n: sigma(sigma(n))-sigma(n)+1 is prime).

%K nonn,changed

%O 1,1

%A _K. D. Bajpai_, Nov 11 2013