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A321576 a(n) is the smallest b > 1 such that b^n - (b-1)^n has all divisors d == 1 (mod n). 1
2, 2, 2, 3, 2, 4, 2, 45, 3, 6, 2, 301, 2, 15, 10, 121, 2, 64, 2, 2101, 7, 12, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For n > 1, a(n) is the least b > 1 such that b^n - (b-1)^n has all prime divisors p == 1 (mod n).

If n is prime, then a(n) = 2. Conjecture: If n is composite, then a(n) > 2.

LINKS

Table of n, a(n) for n=1..23.

MATHEMATICA

primes[n_]:=First@# & /@ FactorInteger[n]; bQ[m_, n_]:=AllTrue[primes[m] -1, Divisible[#, n]&] ; a[n_]:=Module[{b=2}, While[!bQ[b^n - (b-1)^n, n], b++]; b]; Array[a, 100] (* Amiram Eldar, Nov 13 2018 *)

PROG

(PARI) A321576(n)=if(n<4||isprime(n), 2, for(b=2, oo, Set(factor(b^n-(b-1)^n)[, 1]%n)==[1]&&return(b))) \\ M. F. Hasler, Nov 18 2018

CROSSREFS

Cf. A298076.

Sequence in context: A307408 A233539 A317223 * A304101 A278636 A126336

Adjacent sequences:  A321573 A321574 A321575 * A321577 A321578 A321579

KEYWORD

nonn,more

AUTHOR

Thomas Ordowski, Nov 13 2018

EXTENSIONS

a(12)-a(23) from Amiram Eldar, Nov 13 2018

STATUS

approved

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Last modified August 19 08:17 EDT 2019. Contains 326115 sequences. (Running on oeis4.)