A007781 -id:A007781 - cp's OEIS frontend

A068957 Number of prime divisors of n^n - (n-1)^(n-1), counted with multiplicity.

1, 1, 1, 2, 2, 1, 4, 6, 3, 1, 3, 2, 4, 3, 2, 1, 2, 3, 4, 2, 2, 3, 3, 4, 9, 4, 2, 2, 5, 4, 6, 3, 6, 4, 4, 2, 6, 7, 6, 4, 3, 4, 8, 6, 2, 7, 4, 7, 12, 6, 4, 5, 5, 7, 9, 5, 5, 6, 2, 5, 10, 4, 6, 5, 5, 3, 9, 4, 4, 2, 3, 4, 9, 4, 6, 4, 5, 7, 9, 13, 8, 4, 2, 5, 7

Offset: 2

Reinhard Zumkeller, Mar 11 2002

nonn

			A007781(14) = 10809131718965763 = 3 * 61^2 * 968299894201, therefore a(14) = 4.

Cf. A001222, A007781, A068956.

Table[ Apply[ Plus, Transpose[ FactorInteger[n^n - (n - 1)^(n - 1)]] [[ -1]]], {n, 2, 52}]

a(n) = A001222(A007781(n)).

Edited and extended by Robert G. Wilson v, Mar 15 2002

a(53)-a(86) from Amiram Eldar, Feb 06 2020

A114654 Discriminant of the polynomial x^n + x + 1.

Original entry on oeis.org

1, -3, -31, 229, 3381, -43531, -870199, 15953673, 404197705, -9612579511, -295311670611, 8630788777645, 311791207040509, -10809131718965763, -449005897206417391, 18008850183328692241, 845687005960046315793, -38519167813410200811247

Offset: 1

T. D. Noe, Dec 21 2005

sign

Except for the sign, the sequence alternates between the sum and difference of consecutive terms of A000312. x^2+x+1 divides x^n+x+1 for n=2 (mod 3).

Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.

Cf. A000312 (n^n), A007781 (n^n - (n-1)^(n-1)), A056788 (n^n + (n-1)^(n-1)), A086797 (discriminant of the polynomial x^n-x-1).

Table[Discriminant[x^n + x + 1, x], {n, 0, 100}] (* Artur Jasinski, Oct 12 2007 *)

a(n) = poldisc(x^n+x+1); \\ Michel Marcus, Aug 28 2020

for n>1, a(n) = (n^n + (-1)^(n-1) * (n-1)^(n-1)) * (-1)^floor(n/2).

a(n) = (Cos[Pi n/2]+Sin[Pi n/2])(n^n)+(Cos[Pi(n+1)/2]+Sin[Pi(n+1)/2])(n+1)^(n+1). - Artur Jasinski, Oct 12 2007

cp's OEIS Frontend

A068957 Number of prime divisors of n^n - (n-1)^(n-1), counted with multiplicity.

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