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 A091669 a(n) = (2^(n-1)/n!) * Product_{k=1..n-1} (2^k-1). 1
 1, 1, 2, 7, 42, 434, 7812, 248031, 14055090, 1436430198, 267176016828, 91151551074486, 57425477176926180, 67196011936600334340, 146782968474309770332296, 601204690999713530559792879 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Primes p such that 2^p-2 divides a(p) are A216838. - Amiram Eldar and Thomas Ordowski, Jan 16 2020 For odd n > 1, if a(n-1) divides a(n) and n does not divide a(n), then n is a prime (for which 2 is a primitive root, A001122). Composite numbers m such that a(m-1) divides a(m) are the pseudoprimes A001567 and A006935. Numbers n > 1 such that a(m) divides a(n) for all m < n are primes 2, 3, 5, 7, and 13. These are the primes p for which gpf(2^p-2) = p. - Thomas Ordowski, Jan 17 2020 If p is a prime with primitive root 2, A001122, then p | a(p-1) + 2^(p-2). Conjecture: (for n > 2), if n | a(n-1) + 2^(n-2), then n is a prime (A001122). Note that if p is an odd prime for which 2 is not a primitive root, A216838, then p | a(p-1). - Amiram Eldar and Thomas Ordowski, Jan 19 2020 LINKS Amiram Eldar, Table of n, a(n) for n = 1..86 FORMULA a(n) = 2^(n-1)*A005329(n-1)/n!. a(n) = Product_{k=2..n} (2^k-2)/k = Product_{k=2..n} A225101(k)/A159353(k). - Thomas Ordowski, Jan 16 2020 MAPLE seq( (2^(n-1)/n!)*mul(2^j-1, j=1..n-1), n=1..20); # G. C. Greubel, Feb 05 2020 MATHEMATICA Table[QFactorial[n-1, 2] 2^(n-1)/n!, {n, 20}] PROG (PARI) a(n) = (2^(n-1)/n!) * prod(k=1, n-1, 2^k-1); \\ Michel Marcus, Jan 16 2020 (Magma) [1] cat [2^(n-1)/Factorial(n)*&*[(2^k-1):k in [1..n-1]]:n in [2..16]]; // Marius A. Burtea, Jan 16 2020 (Sage) from sage.combinat.q_analogues import q_factorial [2^(n-1)*q_factorial(n-1, 2)/factorial(n) for n in (1..20)] # G. C. Greubel, Feb 05 2020 CROSSREFS Cf. A000142, A001122, A001567, A005329, A006935, A159353, A216838, A225101. Sequence in context: A007065 A352258 A005130 * A108042 A152559 A267239 Adjacent sequences: A091666 A091667 A091668 * A091670 A091671 A091672 KEYWORD nonn AUTHOR Karol A. Penson, Jan 27 2004 EXTENSIONS Corrected and edited by Thomas Ordowski, Jan 16 2020 STATUS approved

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Last modified May 26 04:31 EDT 2024. Contains 372807 sequences. (Running on oeis4.)