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A234936 a(n) is the smallest composite n-Lehmer number. 5
561, 15, 451, 51, 679, 255, 2091, 771, 43435, 3855, 31611, 13107, 272163, 65535, 494211, 196611, 2089011, 983055, 8061051, 3342387, 31580931, 16711935, 126027651, 50529027, 756493591, 252645135, 4446487299, 858993459, 8053383171, 4294967295, 32212942851 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

A number n is a k-Lehmer number if there exists a k such that phi(n) divides (n-1)^k, but not (n-1)^(k-1). The existence of a composite 1-Lehmer number is deemed improbable.

LINKS

Giovanni Resta, Table of n, a(n) for n = 2..36

José María Grau and Antonio M. Oller-Marcén, On k-Lehmer numbers, arXiv:1012.2337 [math.NT], 2010-2012.

José María Grau and Antonio M. Oller-Marcén, On k-Lehmer numbers, Integers, 12(2012), #A37.

Nathan McNew, Radically weakening the Lehmer and Carmichael conditions, arXiv:1210.2001 [math.NT], 2012; International Journal of Number Theory 9 (2013), 1215-1224.

EXAMPLE

a(3) = 15 because 15 is the smallest n such that phi(n) divides (n-1)^3 and does not divide (n-1)^2, i.e., it is the smallest 3-Lehmer number.

MATHEMATICA

a[n_] := a[n] = For[k = 2, True, k++, If[CompositeQ[k], phi = EulerPhi[k]; If[Divisible[(k-1)^n, phi], If[!Divisible[(k-1)^(n-1), phi], Return[k] ]]]]; Table[Print[n, " ", a[n]]; a[n], {n, 2, 20}] (* Jean-François Alcover, Jan 26 2019 *)

PROG

(PARI) a(n) = {x = 2; while (!(!((x-1)^n % eulerphi(x)) && ((x-1)^(n-1) % eulerphi(x))), x++); x; } \\ Michel Marcus, Jan 26 2014

CROSSREFS

Cf. A187731, A173703, A234958.

Sequence in context: A104590 A259211 A265261 * A274443 A247906 A278338

Adjacent sequences:  A234933 A234934 A234935 * A234937 A234938 A234939

KEYWORD

nonn

AUTHOR

Giovanni Resta, Jan 01 2014

STATUS

approved

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Last modified September 22 13:48 EDT 2021. Contains 347607 sequences. (Running on oeis4.)