Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 Jan 26 2024 10:20:33
%S 0,1,0,0,0,0,1,0,1,5,0,0,0,0,1,1,0,0,0,0,1,7,0,0,0,7,8,1,0,0,0,0,0,9,
%T 0,5,1,0,10,1,0,0,0,0,1,1,10,0,1,9,8,7,1,0,0,1,0,1,0,0,0,0,1,1,1,21,0,
%U 0,1,1,0,0,0,0,1,1,1,21,0,0,0,5,0,0,0,1,8,1,12,0,0,1,1,1,14,5,0,0,1,8,12,0,1
%N a(n) = A003415(gcd(A003415(n), A276086(n))), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
%H Antti Karttunen, <a href="/A369449/b369449.txt">Table of n, a(n) for n = 0..16384</a>
%F a(n) = A003415(A327858(n)).
%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 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A369449(n) = A003415(gcd(A003415(n), A276086(n)));
%Y Cf. A003415, A276086, A327858.
%K nonn
%O 0,10
%A _Antti Karttunen_, Jan 26 2024