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A219108
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a(n) = k is the smallest number such that k^3 + 1 has exactly n distinct prime factors.
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3
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0, 1, 3, 5, 17, 59, 101, 563, 2617, 9299, 22109, 132989, 364979, 1970869, 23515229, 109258049, 831731339
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OFFSET
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0,3
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COMMENTS
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This is to exponent 3 as A180278 is to exponent 2.
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LINKS
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FORMULA
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EXAMPLE
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a(0) = 0 because 0^3 + 1 = 1 has no prime factors (being a unit).
a(1) = 1 because 1^3 + 1 = 2 has one prime factor (being a prime).
a(2) = 3 because 3^3 + 1 = 28 has two distinct prime factors {2, 7}.
a(3) = 5 because 5^3 + 1 = 126 has three distinct prime factors {2, 3, 7}.
a(4) = 17 because 17^3 + 1 = 4914 has four distinct prime factors {2, 3, 7, 13}.
a(5) = 59 because 59^3 + 1 = 205380 has five distinct prime factors {2, 3, 5, 7, 163}.
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MATHEMATICA
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k = 1; t = Table[0, {15}]; While[k < 30000001, a = PrimeNu[k^3 + 1]; If[ t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++]; t (* Robert G. Wilson v, Dec 12 2012 *)
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PROG
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(PARI) a(n)=for(k=0, oo, if(omega(k^3+1) == n, return(k))) \\ Andrew Howroyd, Sep 12 2023
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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