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 A219978 Numbers k (>= 1) such that A007781(k-1) = k^k - (k-1)^(k-1) is semiprime. 0
 5, 6, 13, 16, 18, 21, 22, 28, 29, 37, 46, 60, 71, 84 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is to A072164 as semiprimes A001358 are to primes A000040. Can thus be called power difference semiprimes. a(15) >= 115, as 115^115 - 114^114 is a 237-digit composite number with no known factors. - Tyler Busby, Feb 12 2023 LINKS Table of n, a(n) for n=1..14. Eric W. Weisstein, Power Difference Prime FORMULA { k : A007781(k-1) in A001358 }. EXAMPLE 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. MATHEMATICA Flatten[Position[Differences[Table[n^n, {n, 85}]], _?(PrimeOmega[#]==2&)]]+1 (* Harvey P. Dale, Aug 29 2021 *) PROG (PARI) isok(n) = bigomega(n^n - (n-1)^(n-1)) == 2; \\ Michel Marcus, Feb 11 2020 CROSSREFS Cf. A001358, A072164, A007781. Sequence in context: A061437 A067245 A059176 * A326657 A303139 A322611 Adjacent sequences: A219975 A219976 A219977 * A219979 A219980 A219981 KEYWORD nonn,more AUTHOR Jonathan Vos Post, Dec 02 2012 EXTENSIONS a(9)-a(13) from Charles R Greathouse IV, Dec 02 2012 a(14) from Charles R Greathouse IV, Dec 04 2012 STATUS approved

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Last modified May 23 03:55 EDT 2024. Contains 372758 sequences. (Running on oeis4.)