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A219018
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Smallest number k > 0 such that k^n + 1 has exactly n distinct prime factors.
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1
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1, 3, 5, 43, 17, 47, 51, 1697, 59, 512, 521, 3255, 8189, 18951, 656
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OFFSET
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1,2
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COMMENTS
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a(16) > 2 * 10^6; a(18) = 19208. - Daniel Suteu, Feb 06 2023
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LINKS
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EXAMPLE
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a(3) = 5 is the smallest number of the set {k(i)} = {5, 9, 10, 11, 12, 13, 14, 19,….} where k(i)^3 + 1 has exactly 3 distinct prime factors.
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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 09 2012 *)
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PROG
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(PARI) a(n) = my(k=1); while (omega(k^n+1) != n, k++); k; \\ Daniel Suteu, Feb 06 2023
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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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