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A091825
Integers of the form ((k-1)!*2^(k-1) + 1)/k.
1
2, 3, 77, 6583, 337808291, 150922350277, 80658585770586353, 88333886984966359579, 204973945587849174028466087, 2822166959135536313284193618131862069, 9187519016643816926988413546511855483871
OFFSET
0,1
COMMENTS
If p is prime and gcd(q,p)=1 then p divides (p-1)!*q^(p-1) + 1.
EXAMPLE
a(1) = ((1-1)!*2^(1-1) + 1)/1 = 2
((2-1)!*2^(2-1) + 1)/2 = 3/2 is not an integer
a(2) = ((3-1)!*2^(3-1) + 1)/3 = 3
MATHEMATICA
Select[Table[((n-1)! 2^(n-1)+1)/n, {n, 35}], IntegerQ] (* Harvey P. Dale, Mar 24 2011 *)
PROG
(PARI) for (i=1, 100, if(denominator(((i-1)!*2^(i-1)+1)/i)==1, print(((i-1)!*2^(i-1)+1)/i)));
CROSSREFS
Cf. A091824.
Sequence in context: A371269 A377690 A306195 * A166091 A371141 A370993
KEYWORD
nonn
AUTHOR
Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Mar 09 2004
EXTENSIONS
Additional term provided by Harvey P. Dale, Mar 24 2011
STATUS
approved