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A374034
a(n) = A276150(gcd(A276085(n), A328768(n))), where A276150 is the digit sum in primorial base, A276085 is the primorial base log-function, and A328768 is the first primorial based variant of arithmetic derivative.
2
0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 2, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 6, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3
OFFSET
1,8
FORMULA
a(n) = A276150(A374031(n)).
Apparently, a(n) <= A328771(n) for all n >= 1.
PROG
(PARI)
A002110(n) = prod(i=1, n, prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-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); };
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]));
A374034(n) = A276150(gcd(A276085(n), A328768(n)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 27 2024
STATUS
approved