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A328249 Numbers k such that the third arithmetic derivative of A276086(k) is prime.

%I A328249 #13 Jul 02 2021 01:56:20
%S A328249 5,15,21,31,43,79,91,98,104,106,223,229,231,254,255,289,291,301,305,
%T A328249 423,453,456,487,670,674,677,692,702,730,736,2343,2378,2380,2400,2409,
%U A328249 2534,2537,2543,2552,2562,2585,2602,2618,2629,2767,2804,2821,2831,2839,2942,2943,2957,2962,2963,2974,4621,4669,4672,4687,4717,4841,4844
%N A328249 Numbers k such that the third arithmetic derivative of A276086(k) is prime.
%C A328249 Numbers k such that A003415(A003415(A327860(k))) = A099306(A276086(k)) is a prime.
%C A328249 Numbers k such that A276086(k) is in A328239.
%C A328249 For all n, A327969(a(n)) <= 6. This is sharp for example with a(7) = 91.
%H A328249 Antti Karttunen, <a href="/A328249/b328249.txt">Table of n, a(n) for n = 1..1315</a>
%o A328249 (PARI)
%o A328249 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328249 A327860(n) = { my(m=1, i=0, s=0, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), my(e=((n%nextpr)/pr)); m *= (prime(i)^e); s += (e / prime(i)); n-=(n%nextpr)); pr=nextpr); (s*m); };
%o A328249 isA328249(n) = isprime(A003415(A003415(A327860(n))));
%Y A328249 Cf. A003415, A099306, A276086, A327860, A327969, A328239, A328233, A328240.
%K A328249 nonn
%O A328249 1,1
%A A328249 _Antti Karttunen_, Oct 11 2019