Search: a023589 -id:a023589
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5, 7, 11, 15, 23, 27, 35, 39, 47, 59, 63, 75, 83, 87, 95, 107, 119, 123, 135, 143, 147, 159, 167, 179, 195, 203, 207, 215, 219, 227, 255, 263, 275, 279, 299, 303, 315, 327, 335, 347, 359, 363, 383, 387, 395, 399, 423, 447, 455, 459, 467, 479
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OFFSET
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1,1
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LINKS
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FORMULA
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MATHEMATICA
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PROG
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(Haskell)
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CROSSREFS
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Cf. A000040, A005385, A023589, A023590, A023591, A023592, A023593, A072059, A023595, A072060, A072056, A072057, A072058, A072192, A165286, A278230.
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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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A023516
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Number of distinct prime divisors of prime(n)*prime(n-1) - 1.
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1
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0, 1, 2, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 3, 2, 4, 2, 3, 2, 4, 3, 3, 4, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 4, 4, 4, 4, 4, 3, 4, 2, 3, 4, 2, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 2, 4
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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MAPLE
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0, seq(nops(numtheory:-factorset(ithprime(n)*ithprime(n-1)-1)), n=2..120); # Muniru A Asiru, Apr 29 2019
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MATHEMATICA
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Prepend[Table[PrimeNu[Prime[n] Prime[n-1] - 1], {n, 2, 80}], 0] (* Vincenzo Librandi, Apr 27 2019 *)
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PROG
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(Magma) [#PrimeDivisors(NthPrime(n)*(NthPrime(n-1))-1): n in [1..100]]; // Vincenzo Librandi, Apr 27 2019
(PARI) a(n) = if (n==1, 0, omega(prime(n)*prime(n-1) - 1)); \\ Michel Marcus, Apr 30 2019
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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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A072059
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Smallest prime p such that 2*p+1 has n distinct prime factors.
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2
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2, 7, 97, 577, 7507, 217717, 5232727, 75172597, 1617423307, 59844662377, 2750790860317, 109455887488447, 4621264673452927, 218071376383127767, 10914293640945722527, 662082573402158125717, 41249727342503299116997
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OFFSET
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1,1
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COMMENTS
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Note that for each n=1,...,8, the product of the smallest n-1 distinct prime factors of 2*a(n)+1 is p(n)#/2, where p(n)# is the primorial (A002110) of the n-th prime - and the n-th distinct prime factor >= p(n+1). - Rick L. Shepherd, Jul 06 2002
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LINKS
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EXAMPLE
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a(4)=577=A000040(106): 2*577+1 = 1155 = 11*7*5*3, 4 distinct factors.
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PROG
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(PARI) for (n=1, 8, p=1; until(isprime(p) && omega(2*p+1)==n, p++); print1(p, ", "))
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CROSSREFS
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KEYWORD
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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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