A353379 - OEIS

%I #9 Apr 28 2022 20:13:07

%S 0,1,1,2,1,4,1,3,2,4,1,7,1,4,4,4,1,7,1,7,4,4,1,11,2,4,3,7,1,12,1,5,4,

%T 4,4,12,1,4,4,11,1,12,1,7,7,4,1,15,2,7,4,7,1,11,4,11,4,4,1,20,1,4,7,6,

%U 4,12,1,7,4,12,1,19,1,4,7,7,4,12,1,15,4,4,1,20,4,4,4,11,1,20,4,7,4,4,4,21,1,7,7

%N Primepi-based variant of the arithmetic derivative applied to the prime shadow of n.

%H Antti Karttunen, <a href="/A353379/b353379.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F a(n) = A258851(A181819(n)).

%p a:= n-> (m-> m*add(i[2]*numtheory[pi](i[1])/i[1], i=ifactors(m)[2]))

%p         (mul(ithprime(i[2]), i=ifactors(n)[2])):

%p seq(a(n), n=1..120);  # _Alois P. Heinz_, Apr 28 2022

%o (PARI)

%o A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));

%o A258851(n) = (n*sum(i=1, #n=factor(n)~, n[2, i]*primepi(n[1, i])/n[1, i])); \\ From A258851

%o A353379(n) = A258851(A181819(n));

%Y Cf. A181819, A258851.

%Y Cf. also A351942.

%K nonn

%O 1,4

%A _Antti Karttunen_, Apr 28 2022