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A247837 Primes p of the form sigma(2k-1) for a number k.

%I A247837 #29 Jul 10 2025 19:39:43
%S A247837 13,31,307,1093,1723,2801,3541,5113,8011,10303,17293,19531,28057,
%T A247837 30103,30941,86143,88741,147073,292561,459007,492103,552793,579883,
%U A247837 598303,684757,704761,732541,735307,797161,830833,1191373,1204507,1353733,1395943,1424443,1482307
%N A247837 Primes p of the form sigma(2k-1) for a number k.
%C A247837 Supersequence of A247836.
%C A247837 The multiplicity of the sigma-function means that the 2k-1 are odd prime powers 3^2, 5^2, 17^2, 3^6, 41^2,... (A061345), and the fact that sigma(k)>=k means that a numerical search for any candidate p can be limited to the prime powers less than p. - _R. J. Mathar_, Jun 04 2016
%H A247837 Robert Israel, <a href="/A247837/b247837.txt">Table of n, a(n) for n = 1..10000</a>
%F A247837 a(n) = sigma(2*A247820(n)-1) = A000203(2*A247820(n)-1). ***WARNING: This formula is not correct for all n. - _M. F. Hasler_, Nov 16 2014
%F A247837 The first discrepancy in the above formula is at n=11, where a(11) = A000203(2*A247820(12)-1) while A000203(2*A247820(11)-1)=a(12). - _Robert Israel_, Mar 31 2020
%e A247837 Prime 13 is in sequence because there is number 5 such that sigma(2*5-1) = sigma(9) = 13.
%p A247837 isA247837 := proc(n)
%p A247837     local i,opp;
%p A247837     if isprime(n) then
%p A247837         for i from 1 do
%p A247837             opp := A061345(i) ;
%p A247837             if numtheory[sigma](opp) = n then
%p A247837                 return true;
%p A247837             elif opp > n then
%p A247837                 return false;
%p A247837             end if;
%p A247837         end do:
%p A247837     else
%p A247837         false;
%p A247837     end if;
%p A247837 end proc:
%p A247837 for n from 2 do
%p A247837     p := ithprime(n) ;
%p A247837     if isA247837(p) then
%p A247837         printf("%d,\n",p) ;
%p A247837     end if;
%p A247837 end do: # _R. J. Mathar_, Jun 04 2016
%o A247837 (Magma) Sort(b) where b is [a: n in [1..2500000] | IsPrime(a) where a is SumOfDivisors(2*n-1)];
%o A247837 (PARI) for(n=1,10^7,if(isprime(sigma(2*n-1)),print1(sigma(2*n-1),", "))) \\ _Derek Orr_, Sep 25 2014. ***WARNING: This program prints the terms not in correct order. - _M. F. Hasler_, Nov 16 2014
%Y A247837 Cf. A000203, A247836, A247820.
%K A247837 nonn
%O A247837 1,1
%A A247837 _Jaroslav Krizek_, Sep 24 2014
%E A247837 Corrected and edited by _Jaroslav Krizek_, Nov 14 2014