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A048861
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a(n) = n^n - 1.
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23
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0, 3, 26, 255, 3124, 46655, 823542, 16777215, 387420488, 9999999999, 285311670610, 8916100448255, 302875106592252, 11112006825558015, 437893890380859374, 18446744073709551615, 827240261886336764176, 39346408075296537575423, 1978419655660313589123978
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OFFSET
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1,2
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COMMENTS
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a(n) is divisible by (n-1).
Corresponding quotients are a(n)/(n-1) = {1,3,13,85,781,9331, ...} = A023037(n).
p divides a(p-1) for prime p.
p divides a((p-1)/2) for prime p = {3,11,17,19,41,43,59,67,73,83,89,97,...} = A033200 Primes congruent to {1, 3} mod 8; or, odd primes of form x^2+2*y^2.
p divides a((p-1)/3) for prime p = {61,67,73,103,151,193,271,307,367,...} = A014753 3 and -3 are both cubes (one implies other) mod these primes p=1 mod 6.
p divides a((p-1)/4) for prime p = {5,13,17,29,37,41,53,61,73,...} = A002144 Pythagorean primes: primes of form 4n+1.
p divides a((p-1)/5) for prime p = {31,191,251,271,601,641,761,1091,...}.
p divides a((p-1)/6) for prime p = {7,241,313,337,409,439,607,631,727,751,919,937,...}. (End)
For n > 1, a(n) is largest number that can be represented using n digits in the base-n number system. - Chinmaya Dash, Mar 31 2022
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REFERENCES
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M. Le, Primes in the sequences n^n+1 and n^n-1, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, 156-157.
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LINKS
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FORMULA
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EXAMPLE
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Charles T. Le (charlestle(AT)yahoo.com)
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EXTENSIONS
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STATUS
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approved
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