A214811 -id:A214811 - cp's OEIS frontend

A001039 a(n) = (p^p-1)/(p-1) where p = prime(n).

3, 13, 781, 137257, 28531167061, 25239592216021, 51702516367896047761, 109912203092239643840221, 949112181811268728834319677753, 91703076898614683377208150526107718802981

Offset: 1

N. J. A. Sloane

From Luis H. Gallardo, May 27 2022: (Start)
Let r be a root of the trinomial x^p-x-1 in a fixed algebraic closure F of the finite field F_p. Radoux conjectured in 1975 (see References) that a(n) equals the multiplicative order of r in F. The conjecture seems still open.
Moreover, S. Mattarei proved in 2002 that there exists a finite-dimensional non-nilpotent Lie algebra of characteristic p which admits a nonsingular derivation of order a(n) if p is odd and of order 73 if p = 2. (End)

S. Mattarei, The orders of nonsingular derivations of modular Lie algebras, Isr. J. Math., 132 (2002), 265-275.
T. S. Motzkin, Sorting numbers ...: for a link to an annotated scanned version of this paper see A000262.
T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176.
C. Radoux, Nombres de Bell, modulo p premier, et extensions de degré p de F_p. C.R. Acad. Sci. Paris Ser. A-B, 281(21) (1975) A879-A882.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 1..26
J. Levine and R. E. Dalton, Minimum periods, modulo p, of first-order Bell exponential integers, Math. Comp., 16 (1962), 416-423.
W. F. Lunnon, P. A. B. Pleasants, and N. M. Stephens, Arithmetic properties of Bell numbers to a composite modulus I, Acta Arithmetica 35 (1979), pp. 1-16. [From _N. J. A. Sloane_, Feb 07 2009]
P. L. Montgomery, S. Nahm, and S. S. Wagstaff Jr, The period of the Bell numbers modulo a prime, Math. Comp. 79 (2010), 1793-1800.

Cf. A054767, A214811.

for i from 1 to 20 do printf(`%d,`,(ithprime(i)^ithprime(i) -1)/(ithprime(i)-1)) od:

Table[(Prime[n]^Prime[n] - 1)/(Prime[n] - 1), {n, 1, 10}]
(#^#-1)/(#-1)&/@Prime[Range[10]] (* Harvey P. Dale, Apr 09 2016 *)

More terms from James Sellers, Jul 10 2000

A214812 Largest prime factor of (p^p-1)/(p-1) where p = prime(n).

Original entry on oeis.org

3, 13, 71, 4733, 1806113, 1803647, 2699538733, 109912203092239643840221, 1920647391913, 549334763, 568972471024107865287021434301977158534824481, 41903425553544839998158239, 5926187589691497537793497756719, 19825223972382274003506149120708429799166030881820329892377241, 194707033016099228267068299180244011637

Offset: 1

N. J. A. Sloane, Jul 31 2012

nonn

Daniel Suteu, Table of n, a(n) for n = 1..33
T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]

Cf. A001039, A088807, A125135, A212552, A214811.

FactorInteger[#][[-1,1]]&/@Table[(p^p-1)/(p-1),{p,Prime[Range[15]]}] (* Harvey P. Dale, Aug 27 2016 *)

a(n) = my(p=prime(n)); vecmax(factor((p^p-1)/(p-1))[,1]); \\ Daniel Suteu, May 26 2022

a(n) = A006530(A001039(n)). - Daniel Suteu, May 26 2022

A248843 Table read by rows in which row n lists divisors of (p^p-1)/(p-1) where p = prime(n).

Original entry on oeis.org

1, 3, 1, 13, 1, 11, 71, 781, 1, 29, 4733, 137257, 1, 15797, 1806113, 28531167061, 1, 53, 264031, 1803647, 13993643, 95593291, 476218721057, 25239592216021, 1, 10949, 1749233, 2699538733, 19152352117, 29557249587617, 4722122236541789

Offset: 1

Jean-François Alcover, Dec 03 2014

			Table begins:
  [1, 3],
  [1, 13],
  [1, 11, 71, 781],
  [1, 29, 4733, 137257],
  [1, 15797, 1806113, 28531167061],
  [1, 53, 264031, 1803647, 13993643, 95593291, 476218721057, 25239592216021],
  ...

Samuel S. Wagstaff, Aurifeuillian Factorizations and the Period of the Bell Numbers, Math. Comp. 65 (1996), 383-391.
Eric Weisstein's MathWorld, Bell Number
Wikipedia, Bell Number

Cf. A000110, A001039, A054767, A125135, A214810, A214811, A214812.

Table[p = Prime[n]; Divisors[(p^p - 1)/(p - 1)], {n, 1, 10}] // Flatten

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A001039 a(n) = (p^p-1)/(p-1) where p = prime(n).

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A214812 Largest prime factor of (p^p-1)/(p-1) where p = prime(n).

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A248843 Table read by rows in which row n lists divisors of (p^p-1)/(p-1) where p = prime(n).

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