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Minimal number of primorials (A002110) that add to A328768(n), where A328768 is the first primorial based variant of arithmetic derivative.
7

%I #8 Oct 28 2019 20:01:16

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

%H Antti Karttunen, <a href="/A328771/b328771.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(A328768(n)).

%o (PARI)

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

%o 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 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(n) = A276150(A328768(n));

%Y Cf. A002110, A276150, A324888, A328768, A328772.

%K nonn

%O 0,5

%A _Antti Karttunen_, Oct 28 2019