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A219019
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Smallest number k > 1 such that k^n - 1 contains n distinct prime divisors.
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2
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3, 4, 7, 8, 16, 11, 79, 44, 81, 91, 1024, 47, 12769, 389, 256, 413, 46656, 373, 1048576, 1000, 4096, 43541
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OFFSET
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1,1
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COMMENTS
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365000 < a(19) <= 1048576; a(20) = 1000; a(21) = 4096; a(22) = 43541. - Daniel Suteu, Jul 10 2022
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LINKS
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EXAMPLE
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a(3) = 7 is the smallest number of the set {k(i)} = {7, 9, 13, 15, 19, 21, ...} where k(i)^3 - 1 contains 3 distinct prime divisors.
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MAPLE
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with(numtheory) :for n from 1 to 10 do:ii:=0:for k from 1 to 10^10 while(ii=0) do:x:=k^n-1:y:=factorset(x):n1:=nops(y):if n1=n then ii:=1: printf ( "%d %d \n", n, k):
else fi:od:od:
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MATHEMATICA
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L = {}; Do[n = 1; While[Length[FactorInteger[n^k - 1]] != k, n++]; Print@AppendTo[L, n], {k, 15}] (* Giovanni Resta, Nov 10 2012 *)
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PROG
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(PARI) a(n) = my(k=2); while (omega(k^n-1) != n, k++); k; \\ Daniel Suteu, Jul 10 2022
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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