A328772 - OEIS

%I #6 Oct 28 2019 20:01:23

%S 0,0,1,1,2,1,3,1,4,2,5,1,4,1,5,4,4,1,3,1,8,6,7,1,4,4,7,7,10,1,3,1,8,6,

%T 5,6,2,1,5,8,6,1,11,1,12,3,7,1,6,4,7,8,10,1,9,10,16,10,9,1,8,1,5,13,

%U 10,12,15,1,12,10,7,1,8,1,7,5,10,8,11,1,12,6,9,1,8,10,9,12,14,1,9,10,12,10,7,12,6,1,13,17,14,1,11,1,14,9

%N Minimal number of primorials (A002110) that add to A328769(n), where A328769 is the second primorial based variant of arithmetic derivative.

%H Antti Karttunen, <a href="/A328772/b328772.txt">Table of n, a(n) for n = 0..32768</a>

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

%F a(n) = A276150(A328769(n)).

%o (PARI)

%o A002110(n) = prod(i=1,n,prime(i));

%o A328769(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1]))/f[i, 1]));

%o 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 A328772(n) = A276150(A328769(n));

%Y Cf. A002110, A276150, A324888, A328769, A328771.

%K nonn

%O 0,5

%A _Antti Karttunen_, Oct 28 2019