A099498 - OEIS

%I #9 Sep 08 2022 08:45:15

%S 7849,3667649,91171007,2395420006033,11877172892329028459041,

%T 604107995057426434824791,107174878415004743976428761769,

%U 424678439961073471604787362241217,1983672219242345491970468171243171249,10788746499945827829225142589096882612369,42855626937384013751014398588294858582343260060671

%N Semiprimes of the form A007925(n) = n^(n+1)-(n+1)^n.

%e a(1)=7849 because 5^6-6^5=7849=47*167 is a semiprime.

%t Select[Table[n^(n + 1) - (n + 1)^n, {n, 30}], PrimeOmega[#] == 2&] (* _Vincenzo Librandi_, Sep 21 2012 *)

%o (Magma) IsSemiprime:=func<n | &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [3..30] | IsSemiprime(s) where s is n^(n+1)-(n+1)^n]; // _Vincenzo Librandi_, Sep 21 2012

%Y Cf. A007925 n^(n+1)-(n+1)^n, A072179 n^(n+1)-(n+1)^n is prime, A099499 primes of the form n^(n+1)-(n+1)^n, A099497 n^(n+1)-(n+1)^n is a semiprime.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Oct 19 2004

%E a(9)-a(11) from _Vincenzo Librandi_, Sep 21 2012