OFFSET
1,1
COMMENTS
That is, exponents e such that s(s(2^e)) is prime, where s(n) = sigma(n)-n (A001065).
Note that exponents e such that aliquot sequences starting with 2^e end with a prime number at index 1 (exponents e such that s(2^e) is prime) are called "Mersenne exponents" (see A000043).
From Amiram Eldar, Sep 02 2023:
Numbers k such that 2^k - 1 is a term of A037020.
1206 < a(12) <= 2351 (2351 is a term). (End)
LINKS
Jean-Luc Garambois, Aliquot sequences starting on integer powers n^i.
Mersenne forum, Results presentation page.
MATHEMATICA
Select[Range[100], PrimeQ[DivisorSigma[1, 2^# - 1] - 2^# + 1] &] (* Amiram Eldar, Sep 02 2023 *)
PROG
(Sage)
def s(n):
sn = sigma(n) - n
return sn
e = 1
exponents_list = []
while e<=200:
m = 2^e
index = 0
if is_prime(s(s(m))):
exponents_list.append(e)
e+=1
print (exponents_list)
(PARI) f(n) = sigma(n) - n; \\ A001065
isok(k) = ispseudoprime(f(f(2^k))); \\ Michel Marcus, Sep 02 2023
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Jean Luc Garambois, Sep 02 2023
STATUS
approved