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A341933 a(n) = A023896(n) mod A000203(n).

%I A341933 #14 Feb 26 2021 01:54:14
%S A341933 0,1,3,4,4,6,5,1,1,2,7,24,8,18,12,2,10,15,11,38,30,2,13,36,2,30,3,0,
%T A341933 16,48,17,4,42,2,36,34,20,42,20,50,22,60,23,20,72,2,25,12,3,35,24,36,
%U A341933 28,6,20,72,66,2,31,144,32,66,94,8,48,84,35,80,78,120,37,84,38,78,12,108,6,96,41,164
%N A341933 a(n) = A023896(n) mod A000203(n).
%C A341933 a(k) is the sum of totatives of k modulo the sum of divisors of k.
%C A341933 If p is an odd prime, a(p) = (p+3)/2 and a(p^2) = (p-1)/2.
%C A341933 If p is a prime == 5 (mod 6), a(2*p) = 2.
%C A341933 If p is a prime == 1 (mod 6), a(2*p) = 2*p+4.
%C A341933 Are 2, 8 and 9 the only solutions to a(k) = 1?
%H A341933 Robert Israel, <a href="/A341933/b341933.txt">Table of n, a(n) for n = 1..10000</a>
%e A341933 a(6) = 6 because the sum of totatives of 6 is 1+5 = 6, the sum of divisors of 6 is 1+2+3+6 = 12, and 6 mod 12 = 6.
%p A341933 f:= n -> n*numtheory:-phi(n)/2 mod numtheory:-sigma(n):
%p A341933 map(f, [$1..100]);
%t A341933 Array[Mod[# EulerPhi[#]/2 + Boole[# == 1]/2, DivisorSigma[1, #]] &, 80] (* _Michael De Vlieger_, Feb 23 2021 *)
%Y A341933 Cf. A000203, A023896, A239205, A308169.
%K A341933 nonn
%O A341933 1,3
%A A341933 _J. M. Bergot_ and _Robert Israel_, Feb 23 2021