The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
Sequence in context: A007065 A352258 A005130 * A108042 A152559 A267239
KEYWORD
nonn
AUTHOR
Karol A. Penson, Jan 27 2004
EXTENSIONS
Corrected and edited by Thomas Ordowski, Jan 16 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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