A085753 - OEIS

%I #27 Jul 08 2023 11:51:13

%S 3,0,6,3,2,5,6,3,4,3,6,31,6,3,4,1,20,19,28,3,8,3,60,5,16,15,46,3,2,7,

%T 12,13,4,3,18,3,9,3,32,7,6,37,30,61,2,81,26,5,34,79,62,6,44,5,16,15,

%U 10,133,12,31,28,49,26,21,92,43,76,67,38,57,36,43,21,115,2,25,74,179,28,27,52,15

%N Least k such that n^n + k is a semiprime.

%H Sean A. Irvine, <a href="/A085753/b085753.txt">Table of n, a(n) for n = 1..100</a>

%H Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>

%t PrimeFactorExponentsAdded[n_] := Plus @@ Flatten[ Table[ # [[2]], {1}] & /@ FactorInteger[n]]; f[n_] := Block[{k = 0}, While[ PrimeFactorExponentsAdded[n^n + k] != 2, k++ ]; k]; Table[ f[n], {n, 1, 40}]

%o (PARI) a(n) = my(k=0); while (bigomega(n^n+k) != 2, k++); k; \\ _Michel Marcus_, Jul 21 2020

%Y Cf. A001358 (semiprimes), A089542, A089543, A089544.

%K nonn

%O 1,1

%A _Jason Earls_, Jul 21 2003

%E Edited and extended by _Robert G. Wilson v_, Aug 14 2003

%E Corrected and extended by _Ray Chandler_, Nov 22 2003

%E a(69)-a(82) from _Max Alekseyev_, Jun 13 2009

%E a(52) and a(73) corrected by _Sean A. Irvine_, Jul 20 2020