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Primes p of the form sigma(2n-1) for a number n.
7

%I #26 Sep 08 2022 08:46:09

%S 13,31,307,1093,1723,2801,3541,5113,8011,10303,17293,19531,28057,

%T 30103,30941,86143,88741,147073,292561,459007,492103,552793,579883,

%U 598303,684757,704761,732541,735307,797161,830833,1191373,1204507,1353733,1395943,1424443,1482307

%N Primes p of the form sigma(2n-1) for a number n.

%C Supersequence of A247836.

%C The multiplicity of the sigma-function means that the 2n-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 Robert Israel, <a href="/A247837/b247837.txt">Table of n, a(n) for n = 1..10000</a>

%F 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 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 Prime 13 is in sequence because there is number 5 such that sigma(2*5-1) = sigma(9) = 13.

%p isA247837 := proc(n)

%p local i,opp;

%p if isprime(n) then

%p for i from 1 do

%p opp := A061345(i) ;

%p if numtheory[sigma](opp) = n then

%p return true;

%p elif opp > n then

%p return false;

%p end if;

%p end do:

%p else

%p false;

%p end if;

%p end proc:

%p for n from 2 do

%p p := ithprime(n) ;

%p if isA247837(p) then

%p printf("%d,\n",p) ;

%p end if;

%p end do: # _R. J. Mathar_, Jun 04 2016

%o (Magma) Sort(b) where b is [a: n in [1..2500000] | IsPrime(a) where a is SumOfDivisors(2*n-1)]

%o (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 Cf. A000203, A247836, A247820.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Sep 24 2014

%E Corrected and edited by _Jaroslav Krizek_, Nov 14 2014