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A323410 Unitary analog of cototient function A051953: a(n) = n - A047994(n).

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%I A323410 #18 Dec 15 2023 06:19:41
%S A323410 0,1,1,1,1,4,1,1,1,6,1,6,1,8,7,1,1,10,1,8,9,12,1,10,1,14,1,10,1,22,1,
%T A323410 1,13,18,11,12,1,20,15,12,1,30,1,14,13,24,1,18,1,26,19,16,1,28,15,14,
%U A323410 21,30,1,36,1,32,15,1,17,46,1,20,25,46,1,16,1,38,27,22,17,54,1,20,1,42,1,48,21,44,31,18,1,58,19,26,33,48
%N A323410 Unitary analog of cototient function A051953: a(n) = n - A047994(n).
%H A323410 Antti Karttunen, <a href="/A323410/b323410.txt">Table of n, a(n) for n = 1..21210</a>
%H A323410 Antti Karttunen, <a href="/A323410/a323410.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A323410 a(n) = n - A047994(n), where A047994 is unitary phi.
%F A323410 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 1 - A065463 = 0.2955577... . - _Amiram Eldar_, Dec 15 2023
%t A323410 a[n_] := n - Times @@ (Power @@@ FactorInteger[n] - 1); a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Apr 08 2023 *)
%o A323410 (PARI)
%o A323410 A047994(n) = { my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1); };
%o A323410 A323410(n) = (n-A047994(n));
%Y A323410 Cf. A047994, A065463.
%Y A323410 Cf. also A034460, A051953, A323409, A323413.
%K A323410 nonn,easy
%O A323410 1,6
%A A323410 _Antti Karttunen_, Jan 15 2019