login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A263022
a(n) = gcd(n, 1^(n-1) + 2^(n-1) + ... + (n-1)^(n-1)) for n > 1.
1
1, 1, 4, 1, 3, 1, 8, 3, 5, 1, 12, 1, 7, 5, 16, 1, 9, 1, 20, 7, 11, 1, 24, 5, 13, 9, 28, 1, 15, 1, 32, 11, 17, 35, 36, 1, 19, 13, 40, 1, 21, 1, 44, 3, 23, 1, 48, 7, 25, 17, 52, 1, 27, 55, 56, 19, 29, 1, 60, 1, 31, 21, 64, 13, 33, 1, 68, 23, 35, 1, 72, 1, 37, 25, 76, 77, 39, 1, 80, 27, 41, 1, 84, 17, 43, 29, 88, 1, 45, 13, 92, 31, 47, 95, 96
OFFSET
2,3
COMMENTS
a(n) = 1 if and only if n is a prime or n is a Carmichael number.
a(n) is divisible by 4 if n is divisible by 4, otherwise a(n) is odd. - Robert Israel, Oct 08 2015
a(n) = n iff 4|n or n = 35, 55, 77, 95; A121707 ?
a(5005) = 11: this is the first case where a(n) is prime and A001222(n) > 3. - Altug Alkan, Oct 08 2015
LINKS
FORMULA
a(4n) = 4n.
a(n) = gcd(A031971(n-1), n). - Michel Marcus, Oct 08 2015
MAPLE
f:= n -> igcd(n, add(j &^(n-1) mod n, j=1..n-1)):
seq(f(n), n=2..1000); # Robert Israel, Oct 08 2015
MATHEMATICA
Table[GCD[n, Total@ Map[#^(n - 1) &, Range[n - 1]]], {n, 2, 96}] (* Michael De Vlieger, Oct 08 2015 *)
PROG
(PARI) vector(100, n, gcd(n+1, sum(k=1, n, k^n))) \\ Altug Alkan, Oct 08 2015
CROSSREFS
Cf. A002997 (see my Oct 09 2013 comment).
Sequence in context: A353776 A292269 A010127 * A326690 A353275 A340079
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Oct 07 2015
STATUS
approved