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%I #32 Mar 03 2024 10:15:31
%S 4,9,16,27,49,64,121,125,169,289,1681,1849,2401,3481,4913,5329,11881,
%T 12769,16129,18769,24649,29791,32041,32761,38809,39601,44521,63001,
%U 69169,76729,78125,79507,85849,96721,124609,130321,134689,143641,167281,175561,187489,237169,316969,326041,332929,380689,383161,434281,491401
%N Composite numbers k such that tau(k^(k-1)) is a prime.
%C A proper subset of A280257 and of A025475.
%H Robert G. Wilson v, <a href="/A283549/b283549.txt">Table of n, a(n) for n = 1..10556</a>
%t k = 1; lst = {}; While[k < 100001, If [ !PrimeQ@ k && PrimeQ[ DivisorSigma[0, k^(k -1)]], AppendTo[lst, k]]; k++]; lst (* or *)
%t mx = 10^6; Union@ Flatten@ Reap[ Do[ Sow@ Select[ Prime[ Range[ PrimePi[ mx^(1/e) ]]]^e, PrimeQ[1 + e (#-1)] &], {e, 2, Log2[mx]}]][[2, 1]] (* _Giovanni Resta_, Mar 10 2017 *)
%o (PARI) is(n)=!isprime(n) && ispseudoprime(numdiv(n^(n-1))) \\ _Charles R Greathouse IV_, Mar 10 2017
%Y Cf. A280257, A025475.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Mar 10 2017
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