|
|
A247837
|
|
Primes p of the form sigma(2n-1) for a number n.
|
|
7
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
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
|
|
|
FORMULA
|
|
|
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
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;
|
|
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
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|