This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A219978 #30 Feb 16 2025 08:33:18
%S A219978 5,6,13,16,18,21,22,28,29,37,46,60,71,84
%N A219978 Numbers k (>= 1) such that A007781(k-1) = k^k - (k-1)^(k-1) is semiprime.
%C A219978 This is to A072164 as semiprimes A001358 are to primes A000040. Can thus be called power difference semiprimes.
%C A219978 a(15) >= 115, as 115^115 - 114^114 is a 237-digit composite number with no known factors. - _Tyler Busby_, Feb 12 2023
%H A219978 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/PowerDifferencePrime.html">Power Difference Prime</a>
%F A219978 { k : A007781(k-1) in A001358 }.
%e A219978 a(1) = 5 because 5^5 - 4^4 = 2869 = 19 * 151 is semiprime.
%e A219978 a(2) = 6 because 6^6 - 5^5 = 43531 = 101 * 431.
%e A219978 a(3) = 13 because 13^13 - 12^12 = 293959006143997 = 28201 * 10423708597.
%e A219978 a(4) = 16 because 16^16 - 15^15 = 18008850183328692241 = 109 * 165218809021364149.
%t A219978 Flatten[Position[Differences[Table[n^n,{n,85}]],_?(PrimeOmega[#]==2&)]]+1 (* _Harvey P. Dale_, Aug 29 2021 *)
%o A219978 (PARI) isok(n) = bigomega(n^n - (n-1)^(n-1)) == 2; \\ _Michel Marcus_, Feb 11 2020
%Y A219978 Cf. A001358, A072164, A007781.
%K A219978 nonn,more
%O A219978 1,1
%A A219978 _Jonathan Vos Post_, Dec 02 2012
%E A219978 a(9)-a(13) from _Charles R Greathouse IV_, Dec 02 2012
%E A219978 a(14) from _Charles R Greathouse IV_, Dec 04 2012