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a(n) = A276085(A370117(n)), where A370117(n) is the denominator of n/A276086(A003415(n)), A003415 is the arithmetic derivative, A276086 is the primorial base exp-function, and A276085 is its inverse, the primorial base log-function.
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%I #7 Feb 11 2024 14:20:21

%S 0,0,0,1,4,1,2,1,12,6,0,1,14,1,8,0,32,1,18,1,18,8,12,1,42,4,14,25,2,1,

%T 30,1,80,12,18,6,60,1,20,14,62,1,8,1,48,31,24,1,110,14,32,18,56,1,78,

%U 10,62,20,30,1,90,1,32,19,192,12,60,1,72,24,22,1,156,1,38,43,80,18,68,1,170,108,42,1,92,16,44

%N a(n) = A276085(A370117(n)), where A370117(n) is the denominator of n/A276086(A003415(n)), A003415 is the arithmetic derivative, A276086 is the primorial base exp-function, and A276085 is its inverse, the primorial base log-function.

%H Antti Karttunen, <a href="/A370120/b370120.txt">Table of n, a(n) for n = 0..16384</a>

%F a(n) = A276085(A370117(n)).

%o (PARI)

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

%o A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A370120(n) = { my(u=A276086(A003415(n))); A276085(u/gcd(n, u)); };

%Y Cf. A003415, A276085, A276086, A327859, A369964, A370115 (positions of 0's), A370117.

%K nonn

%O 0,5

%A _Antti Karttunen_, Feb 11 2024