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A219978
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Numbers n (>= 1) such that A007781(n-1) = n^n - (n-1)^(n-1) is semiprime.
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0
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5, 6, 13, 16, 18, 21, 22, 28, 29, 37, 46, 60, 71, 84
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OFFSET
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1,1
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COMMENTS
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This is to A072164 as semiprimes A001358 are to primes A000040. Can thus be called power difference semiprimes.
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LINKS
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Table of n, a(n) for n=1..14.
Eric W. Weisstein, Power Difference Prime
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FORMULA
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{ n : A007781(n-1) in {A001358} }.
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EXAMPLE
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a(1) = 5 because 5^5 - 4^4 = 2869 = 19 * 151 is semiprime.
a(2) = 6 because 6^6 - 5^5 = 43531 = 101 * 431.
a(3) = 13 because 13^13 - 12^12 = 293959006143997 = 28201 * 10423708597.
a(4) = 16 because 16^16 - 15^15 = 18008850183328692241 = 109 * 165218809021364149.
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MATHEMATICA
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Flatten[Position[Differences[Table[n^n, {n, 85}]], _?(PrimeOmega[#]==2&)]]+1 (* Harvey P. Dale, Aug 29 2021 *)
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PROG
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(PARI) isok(n) = bigomega(n^n - (n-1)^(n-1)) == 2; \\ Michel Marcus, Feb 11 2020
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CROSSREFS
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Cf. A001358, A072164, A007781.
Sequence in context: A061437 A067245 A059176 * A326657 A303139 A322611
Adjacent sequences: A219975 A219976 A219977 * A219979 A219980 A219981
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KEYWORD
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nonn,more
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AUTHOR
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Jonathan Vos Post, Dec 02 2012
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EXTENSIONS
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a(9)-a(13) from Charles R Greathouse IV, Dec 02 2012
a(14) from Charles R Greathouse IV, Dec 04 2012
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STATUS
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approved
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