cp's OEIS Frontend

A353577 Arithmetic derivative without its inherited divisor applied to the prime shadow of the primorial base exp-function: a(n) = A342001(A181819(A276086(n))).

%I A353577 #18 Apr 30 2022 22:51:37
%S A353577 0,1,1,2,1,5,1,2,2,3,5,8,1,5,5,8,2,7,1,7,7,12,8,31,1,9,9,16,10,41,1,2,
%T A353577 2,3,5,8,2,3,3,4,8,11,5,8,8,11,7,10,7,12,12,17,31,46,9,16,16,23,41,62,
%U A353577 1,5,5,8,2,7,5,8,8,11,7,10,2,7,7,10,3,9,8,31,31,46,13,41,10,41,41,62,17,55,1,7,7,12,8
%N A353577 Arithmetic derivative without its inherited divisor applied to the prime shadow of the primorial base exp-function: a(n) = A342001(A181819(A276086(n))).
%H A353577 Antti Karttunen, <a href="/A353577/b353577.txt">Table of n, a(n) for n = 0..11550</a>
%H A353577 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A353577 a(n) = A342001(A328835(n)) = A351945(A276086(n)) = A342001(A181819(A276086(n))).
%F A353577 a(n) = A353576(n) / A353524(n).
%o A353577 (PARI)
%o A353577 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A353577 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A353577 A342001(n) = (A003415(n) / A003557(n));
%o A353577 A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
%o A353577 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A353577 A353577(n) = A342001(A181819(A276086(n)));
%Y A353577 Cf. A003415, A003557, A181819, A276086, A328835, A342001, A351942, A351945, A353524, A353576.
%Y A353577 Cf. A060735 (positions of 1's).
%Y A353577 Cf. also A342002, A351954 (similar or analogous definitions).
%K A353577 nonn,base,easy,look
%O A353577 0,4
%A A353577 _Antti Karttunen_, Apr 30 2022