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A248792 Numbers n such that sigma(n) - 1 is a prime p.

%I A248792 #27 Apr 30 2025 21:04:43
%S A248792 2,3,5,6,7,10,11,13,14,15,17,19,20,21,23,24,26,29,30,31,33,34,35,37,
%T A248792 38,40,41,43,44,46,47,51,52,53,55,57,58,59,60,61,63,65,67,71,73,74,76,
%U A248792 78,79,83,84,85,86,88,89,90,92,93,96,97,101,103,105,107,109
%N A248792 Numbers n such that sigma(n) - 1 is a prime p.
%C A248792 Union of primes (A000040) and terms of A066073 (composites).
%C A248792 Numbers n such that A039653(n) is prime.
%C A248792 Corresponding values of primes p are in A248793.
%H A248792 Michael De Vlieger, <a href="/A248792/b248792.txt">Table of n, a(n) for n = 1..10000</a>
%H A248792 OEIS Wiki, <a href="https://oeis.org/wiki/Cyclotomic Polynomials at x=n, n! and sigma(n)">Cyclotomic Polynomials at x=n, n! and sigma(n)</a>
%e A248792 6 is in sequence because sigma(6) - 1 = 12 - 1 = 11 (prime).
%p A248792 with(numtheory): A248792:=n->`if`(isprime(sigma(n)-1), n, NULL): seq(A248792(n), n=1..200); # _Wesley Ivan Hurt_, Jul 09 2015
%t A248792 Select[Range[110], PrimeQ[DivisorSigma[1, #] - 1] &] (* _Vincenzo Librandi_, Nov 02 2014 *)
%o A248792 (Magma) [n: n in[1..1000] | IsPrime(SumOfDivisors(n) - 1)];
%o A248792 (PARI) for(n=1,10^3,if(isprime(sigma(n)-1),print1(n,", "))) \\ _Derek Orr_, Nov 01 2014
%Y A248792 Cf. A000203 (sum of divisors), A000040 (primes).
%Y A248792 Cf. A039653 (sigma(n)-1), A066073 (subsequence of composites), A248793.
%Y A248792 Cf. A065512 (numbers n such that sigma(n) + 1 is prime).
%K A248792 nonn,easy
%O A248792 1,1
%A A248792 _Jaroslav Krizek_, Nov 01 2014