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A253628 Psi(n) mod n, where Psi is the Dedekind psi function (A001615).

%I A253628 #18 Jan 10 2015 04:23:52
%S A253628 0,1,1,2,1,0,1,4,3,8,1,0,1,10,9,8,1,0,1,16,11,14,1,0,5,16,9,20,1,12,1,
%T A253628 16,15,20,13,0,1,22,17,32,1,12,1,28,27,26,1,0,7,40,21,32,1,0,17,40,23,
%U A253628 32,1,24,1,34,33,32,19,12,1,40,27,4,1,0,1,40,45
%N A253628 Psi(n) mod n, where Psi is the Dedekind psi function (A001615).
%C A253628 a(n) = A054024(n) when n is squarefree.
%C A253628 Indices of 1 appear to be given by primes A000040 (see conjecture in A068494). The (weaker) statement that a(prime(i)) = 1 is a direct consequence of the multiplicity of A001615.
%C A253628 a(n) = 0 if n is a member of A187778.
%H A253628 Michael De Vlieger, <a href="/A253628/b253628.txt">Table of n, a(n) for n = 1..10000</a>
%F A253628 a(n) = A001615(n) mod n.
%e A253628 A001615(12) = 24 and 24 == 0 (mod 12) so a(12) = 0.
%e A253628 A001615(15) = 24 and 24 == 9 (mod 15) so a(15) = 9.
%p A253628 A253628 := proc(n)
%p A253628     modp(A001615(n),n) ;
%p A253628 end proc: # _R. J. Mathar_, Jan 09 2015
%t A253628 a253628[n_] :=
%t A253628 Mod[DirichletConvolve[j, MoebiusMu[j]^2, j, #], #] & /@ Range@n; a253628[75] (* _Michael De Vlieger_, Jan 07 2015, after _Jan Mangaldan_ at A001615 *)
%o A253628 (Sage)
%o A253628 [(n*mul(1+1/p for p in prime_divisors(n)))%n for n in [1..100]]
%Y A253628 Cf. A001615, A068494, A054024, A006093, A187778.
%K A253628 nonn
%O A253628 1,4
%A A253628 _Tom Edgar_, Jan 06 2015