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A253628
Psi(n) mod n, where Psi is the Dedekind psi function (A001615).
1
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
1,4
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.
LINKS
FORMULA
a(n) = A001615(n) mod n.
EXAMPLE
A001615(12) = 24 and 24 == 0 (mod 12) so a(12) = 0.
A001615(15) = 24 and 24 == 9 (mod 15) so a(15) = 9.
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 *)
PROG
(Sage)
[(n*mul(1+1/p for p in prime_divisors(n)))%n for n in [1..100]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Tom Edgar, Jan 06 2015
STATUS
approved