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A328232 Numbers whose arithmetic derivative (A003415) is a primorial number, including cases where it is the first primorial, A002110(0) = 1.

%I A328232 #18 Oct 10 2019 20:32:03
%S A328232 2,3,5,7,9,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,
%T A328232 89,97,101,103,107,109,113,127,131,137,139,149,151,157,161,163,167,
%U A328232 173,179,181,191,193,197,199,209,211,221,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317
%N A328232 Numbers whose arithmetic derivative (A003415) is a primorial number, including cases where it is the first primorial, A002110(0) = 1.
%C A328232 Numbers n such that A327859(n) = A276086(A003415(n)) is a prime.
%H A328232 Antti Karttunen, <a href="/A328232/b328232.txt">Table of n, a(n) for n = 1..10000</a>
%H A328232 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%o A328232 (PARI)
%o A328232 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328232 A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
%o A328232 A327859(n) = A276086(A003415(n));
%o A328232 isA328232(n) = isprime(A327859(n));
%Y A328232 Cf. A002110, A003415, A024451 (arith. deriv. of primorials), A068346, A276086, A327859, A328233.
%Y A328232 Union of A000040 and A327978 (gives the composite terms).
%Y A328232 Differs from A189710 for the first time by having term a(39) = 161, which is not included in A189710, while A189710(44) = 185 is the first term in latter that is not included here.
%K A328232 nonn
%O A328232 1,1
%A A328232 _Antti Karttunen_, Oct 09 2019