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A144671
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Numbers n such that omega(n) = omega(2^n-1), where omega = A001221 = number of distinct prime factors.
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1
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1, 2, 3, 5, 6, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607
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OFFSET
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1,2
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COMMENTS
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A prime p is in this sequence iff 2^p-1 is prime, thus iff p is in A000043 (Mersenne prime exponents), which is a subsequence of this one - and of A155990. The latter contains (some) powers of primes, which cannot be the case here.
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LINKS
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EXAMPLE
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a(1) = 1 is in this sequence since omega(1) = 0 = omega(2^1-1). Elements of A000043 are primes p such that 2^p-1, they are in this sequence since omega(p) = 1 = omega(2^p-1). a(5) = 6 is in this sequence since omega(6) = #{2,3} = 2 = omega(2^6-1) = #{3,7}.
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MATHEMATICA
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Select[Range[700], PrimeNu[#]==PrimeNu[2^#-1]&] (* Harvey P. Dale, Jan 04 2018 *)
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PROG
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(PARI) is_A144671(n)={ omega(n)==omega(2^n-1) }
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CROSSREFS
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KEYWORD
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more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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