OFFSET
1,1
COMMENTS
Supersequence of A247836.
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
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
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
EXAMPLE
Prime 13 is in sequence because there is number 5 such that sigma(2*5-1) = sigma(9) = 13.
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
PROG
(Magma) Sort(b) where b is [a: n in [1..2500000] | IsPrime(a) where a is SumOfDivisors(2*n-1)]
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Sep 24 2014
EXTENSIONS
Corrected and edited by Jaroslav Krizek, Nov 14 2014
STATUS
approved