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

13, 31, 307, 1093, 1723, 2801, 3541, 5113, 8011, 10303, 17293, 19531, 28057, 30103, 30941, 86143, 88741, 147073, 292561, 459007, 492103, 552793, 579883, 598303, 684757, 704761, 732541, 735307, 797161, 830833, 1191373, 1204507, 1353733, 1395943, 1424443, 1482307

Offset: 1

Author

Jaroslav Krizek, Sep 24 2014

Keywords

• nonn

Comments

Supersequence of A247836.

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

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A247836, A247820.

Programs

Magma

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

Maple

isA247837 := proc(n)
    local i,opp;
    if isprime(n) then
        for i from 1 do
            opp := A061345(i) ;
            if numtheory[sigma](opp) = n then
                return true;
            elif opp > n then
                return false;
            end if;
        end do:
    else
        false;
    end if;
end proc:
for n from 2 do
    p := ithprime(n) ;
    if isA247837(p) then
        printf("%d,\n",p) ;
    end if;
end do: # R. J. Mathar, Jun 04 2016

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

Formula

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

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

Extensions

Corrected and edited by Jaroslav Krizek, Nov 14 2014