cp's OEIS Frontend

A351573 Arithmetic derivative of the largest unitary divisor of n that is an exponentially odd number.

%I A351573 #11 Feb 25 2022 17:03:39
%S A351573 0,1,1,0,1,5,1,12,0,7,1,1,1,9,8,0,1,1,1,1,10,13,1,44,0,15,27,1,1,31,1,
%T A351573 80,14,19,12,0,1,21,16,68,1,41,1,1,1,25,1,1,0,1,20,1,1,81,16,92,22,31,
%U A351573 1,8,1,33,1,0,18,61,1,1,26,59,1,12,1,39,1,1,18,71,1,1,0,43,1,10,22,45,32,140,1,7,20,1,34
%N A351573 Arithmetic derivative of the largest unitary divisor of n that is an exponentially odd number.
%H A351573 Antti Karttunen, <a href="/A351573/b351573.txt">Table of n, a(n) for n = 1..20000</a>
%F A351573 a(n) = A003415(A350389(n)).
%t A351573 f1[p_, e_] := If[OddQ[e], p^e, 1]; f2[p_, e_] := If[OddQ[e], e/p, 0]; a[1] = 0; a[n_] := (Times @@ f1 @@@ (f = FactorInteger[n])) * (Plus @@ f2 @@@ f); Array[a, 100] (* _Amiram Eldar_, Feb 23 2022 *)
%o A351573 (PARI)
%o A351573 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A351573 A350389(n) = { my(m=1, f=factor(n)); for(k=1,#f~,if(1==(f[k,2]%2), m *= (f[k,1]^f[k,2]))); (m); };
%o A351573 A351573(n) = A003415(A350389(n));
%Y A351573 Cf. A003415, A350388, A268335 (exponentially odd numbers), A351571, A351572.
%K A351573 nonn
%O A351573 1,6
%A A351573 _Antti Karttunen_, Feb 23 2022