A328240 - OEIS

%I #13 Jul 02 2021 01:54:07

%S 4,12,32,35,40,46,47,65,67,68,71,73,74,76,220,221,225,226,227,250,256,

%T 257,276,283,284,420,421,425,426,436,486,489,494,2324,2325,2352,2370,

%U 2387,2525,2530,2531,2555,2560,2565,2566,2583,2596,2734,2739,2760,2765,2769,2771,2773,2795,2797,2798,2803,4623,4627,4628

%N Numbers k such that the second arithmetic derivative of A276086(k) is prime.

%C Numbers k for which A003415(A327860(k)) = A003415(A003415(A276086(k))) is a prime.

%C Numbers k such that A276086(k) is in A192192, or equally, k such that A327860(k) is in A157037.

%H Antti Karttunen, <a href="/A328240/b328240.txt">Table of n, a(n) for n = 1..1217</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F For all n, a(A327969(n)) <= 5.

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o 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 isA328240(n) = isprime(A003415(A327860(n)));

%Y Cf. A003415, A157037, A192192, A276086, A327860, A327969, A328233.

%Y Subsequence of A328116 and of A328242.

%K nonn

%O 1,1

%A _Antti Karttunen_, Oct 10 2019