cp's OEIS Frontend

A328771 Minimal number of primorials (A002110) that add to A328768(n), where A328768 is the first primorial based variant of arithmetic derivative.

%I A328771 #8 Oct 28 2019 20:01:16
%S A328771 0,0,1,1,2,1,2,1,2,2,5,1,4,1,4,6,2,1,3,1,4,6,6,1,6,2,5,5,10,1,6,1,6,8,
%T A328771 7,8,6,1,6,8,6,1,5,1,8,7,8,1,6,2,9,6,10,1,8,8,8,6,9,1,10,1,4,9,8,10,
%U A328771 13,1,8,8,14,1,10,1,5,5,10,12,10,1,6,2,7,1,8,10,6,10,14,1,5,14,8,6,8,12,6,1,9,15,8,1,16,1,14,7
%N A328771 Minimal number of primorials (A002110) that add to A328768(n), where A328768 is the first primorial based variant of arithmetic derivative.
%H A328771 Antti Karttunen, <a href="/A328771/b328771.txt">Table of n, a(n) for n = 0..32768</a>
%H A328771 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A328771 a(n) = A276150(A328768(n)).
%o A328771 (PARI)
%o A328771 A002110(n) = prod(i=1,n,prime(i));
%o A328771 A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1])-1)/f[i, 1]));
%o A328771 A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
%o A328771 A328771(n) = A276150(A328768(n));
%Y A328771 Cf. A002110, A276150, A324888, A328768, A328772.
%K A328771 nonn
%O A328771 0,5
%A A328771 _Antti Karttunen_, Oct 28 2019