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a(n) = A003415(A276085(n)), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.
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%I #11 Jun 22 2024 18:02:31

%S 0,0,1,1,5,1,31,1,4,1,247,4,2927,1,12,4,40361,1,716167,12,80,1,

%T 14117683,1,16,1,5,80,334406399,6,9920878441,1,216,568,60,5,

%U 314016924901,33975,3740,6,11819186711467,14,492007393304957,216,7,28300,21460568175640361,5,92,1,60080,3740,1021729465586766997,1,540,14

%N a(n) = A003415(A276085(n)), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

%H Antti Karttunen, <a href="/A373842/b373842.txt">Table of n, a(n) for n = 1..481</a>

%F For n >= 1, a(A000040(n)) = A024451(n-1).

%o (PARI)

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

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

%o A373842(n) = A003415(A276085(n));

%Y Cf. A003415, A024451, A276085, A373843 [= gcd(n, a(n))], A373846 (positions of 1's), A373847 [k such that a(n)<=k], A373848.

%K nonn

%O 1,5

%A _Antti Karttunen_, Jun 20 2024