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A278741
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Odd numbers k such that tau(k-1) is a prime.
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3
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3, 5, 17, 65, 1025, 4097, 65537, 262145, 4194305, 268435457, 1073741825, 68719476737, 1099511627777, 4398046511105, 70368744177665, 4503599627370497, 288230376151711745, 1152921504606846977, 73786976294838206465, 1180591620717411303425, 4722366482869645213697
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OFFSET
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1,1
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COMMENTS
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tau(k) = A000005(k) = the number of divisors of k.
Conjecture: prime terms are in A249759: 3, 5, 17, 65537, ...
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LINKS
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FORMULA
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sigma(a(n)-1) = A001348(n), i.e., Mersenne numbers.
tau(a(n)-1) = A000040(n), i.e., all primes; a(n) = the smallest odd number k such that tau(a(n)-1) = prime(n) = A000040(n).
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EXAMPLE
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Odd number 65 is in the sequence because tau(64) = 7 (prime).
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PROG
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(Magma) [n: n in[2..10000000] | IsOdd(n) and IsPrime(NumberOfDivisors(n-1))]
(PARI) isok(n) = (n % 2) && isprime(numdiv(n-1)); \\ Michel Marcus, Nov 27 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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