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A294179 a(n) is the smallest k with n prime factors such that p^k == p (mod k) for every prime p dividing k. 0
2, 65, 561, 41041, 825265, 321197185 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All the terms are squarefree. Are all composite terms odd?

Conjecture: the sequence contains only finitely many Carmichael numbers, A006931. What is the smallest n >= 3 for which a(n) is not a Carmichael number? For n >= 3, a(n) <= A006931(n). Maybe a(7) < A006931(7).

LINKS

Table of n, a(n) for n=1..6.

MAPLE

for k from 2 to 10^6 do

  if numtheory:-issqrfree(k) then

    ps := numtheory:-factorset(k);

    n := nops(ps);

    if not assigned(A[n]) and andmap(p -> p &^ k -p mod k = 0, ps) then

      A[n] := k;

    end if

  end if;

end do:

seq(A[i], i=1..max(map(op, [indices(A)]))); # Robert Israel, Feb 11 2018

MATHEMATICA

With[{s = Select[Range[10^6], Function[k, AllTrue[FactorInteger[k][[All, 1]], PowerMod[#, k, k] == Mod[#, k] &]]]}, Select[Table[SelectFirst[s, PrimeOmega@ # == n &], {n, 5}], IntegerQ]] (* Michael De Vlieger, Feb 20 2018 *)

CROSSREFS

Cf. A006931, A285549, A294169.

Sequence in context: A303376 A041511 A156651 * A002604 A294273 A199145

Adjacent sequences:  A294176 A294177 A294178 * A294180 A294181 A294182

KEYWORD

nonn,more,hard

AUTHOR

Thomas Ordowski, Feb 11 2018

STATUS

approved

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Last modified September 20 12:41 EDT 2019. Contains 327237 sequences. (Running on oeis4.)