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A207080 The smallest Carmichael number k such that phi(k) does not divide (k-1)^n, where phi is the Euler totient function. 2
561, 2821, 838201, 41471521, 45496270561, 776388344641, 344361421401361, 375097930710820681, 330019822807208371201 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: phi(a(n)) divides (a(n)-1)^(n+1).

a(10) <= 9645020063586019926451. - Daniel Suteu, Dec 25 2020

LINKS

Table of n, a(n) for n=1..9.

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 (2012).

PROG

(PARI) is_c(n) = { my(f); bittest(n, 0) && !for(i=1, #f=factor(n)~, (f[2, i]==1 && n%(f[1, i]-1)==1)||return) && #f>1; }

isok(k, n) = ((k-1)^n % eulerphi(k)) != 0;

a(n) = my(k=1); while (!(is_c(k) && isok(k, n)), k++); k; \\ Michel Marcus, Dec 25 2020

CROSSREFS

Cf. A000010, A002997 (Carmichael numbers), A173703.

Sequence in context: A293622 A322130 A354609 * A339875 A290945 A063400

Adjacent sequences:  A207077 A207078 A207079 * A207081 A207082 A207083

KEYWORD

nonn,more

AUTHOR

José María Grau Ribas, Feb 15 2012

EXTENSIONS

a(7)-a(9) from Richard Pinch, Feb 18 2012

STATUS

approved

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Last modified August 7 21:39 EDT 2022. Contains 355995 sequences. (Running on oeis4.)