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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jan 15 2019

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..21210
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A047994, A065463.

Cf. also A034460, A051953, A323409, A323413.

Programs

Mathematica

a[n_] := n - Times @@ (Power @@@ FactorInteger[n] - 1); a[1] = 0; Array[a, 100] (* Amiram Eldar, Apr 08 2023 *)

PARI

A047994(n) = { my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1); };
A323410(n) = (n-A047994(n));

Formula

a(n) = n - A047994(n), where A047994 is unitary phi.

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 1 - A065463 = 0.2955577... . - Amiram Eldar, Dec 15 2023