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A365351
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Exponents e such that the aliquot sequence starting with 2^e ends with a prime number at index 2.
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0
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6, 11, 18, 27, 41, 74, 157, 197, 294, 549, 581
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OFFSET
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1,1
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COMMENTS
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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).
Numbers k such that 2^k - 1 is a term of A037020.
1206 < a(12) <= 2351 (2351 is a term). (End)
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LINKS
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MATHEMATICA
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Select[Range[100], PrimeQ[DivisorSigma[1, 2^# - 1] - 2^# + 1] &] (* Amiram Eldar, Sep 02 2023 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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