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A328771
Minimal number of primorials (A002110) that add to A328768(n), where A328768 is the first primorial based variant of arithmetic derivative.
7
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, 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, 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
OFFSET
0,5
FORMULA
a(n) = A276150(A328768(n)).
PROG
(PARI)
A002110(n) = prod(i=1, n, prime(i));
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]));
A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 28 2019
STATUS
approved