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

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, 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, 32, 1, 24, 1, 34, 33, 32, 19, 12, 1, 40, 27, 4, 1, 0, 1, 40, 45

Offset: 1

Author

Tom Edgar, Jan 06 2015

Keywords

• nonn

Comments

a(n) = A054024(n) when n is squarefree.

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.

a(n) = 0 if n is a member of A187778.

Examples

			A001615(12) = 24 and 24 == 0 (mod 12) so a(12) = 0.
A001615(15) = 24 and 24 == 9 (mod 15) so a(15) = 9.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001615, A068494, A054024, A006093, A187778.

Programs

Maple

A253628 := proc(n)
    modp(A001615(n),n) ;
end proc: # R. J. Mathar, Jan 09 2015

Mathematica

a253628[n_] :=
Mod[DirichletConvolve[j, MoebiusMu[j]^2, j, #], #] & /@ Range@n; a253628[75] (* Michael De Vlieger, Jan 07 2015, after Jan Mangaldan at A001615 *)

Sage

[(n*mul(1+1/p for p in prime_divisors(n)))%n for n in [1..100]]

Formula

a(n) = A001615(n) mod n.