A054586 a(n) = Sum_{d|2n+1} phi(d)*mu(d).

1, -1, -3, -5, -1, -9, -11, 3, -15, -17, 5, -21, -3, -1, -27, -29, 9, 15, -35, 11, -39, -41, 3, -45, -5, 15, -51, 27, 17, -57, -59, 5, 33, -65, 21, -69, -71, 3, 45, -77, -1, -81, 45, 27, -87, 55, 29, 51, -95, 9, -99, -101, -15, -105, -107, 35, -111, 63, 11, 75, -9

Offset

0,3

References

David M. Burton, Elementary Number Theory, Allyn and Bacon Inc., Boston, MA, 1976, p. 152.

Links

Table of n, a(n) for n=0..60.

Formula

a(n) = A276833(2*n+1). - Amiram Eldar, Aug 12 2023

Mathematica

a[n_] := DivisorSum[2*n+1, MoebiusMu[#]*EulerPhi[#]&]; Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Dec 03 2015 *)
f[p_, e_] := 2-p; a[n_] := Times @@ f @@@ FactorInteger[2*n+1]; Array[a, 100, 0] (* Amiram Eldar, Aug 12 2023 *)

Prog

(PARI) j=[]; for(n=0, 200, j=concat(j, sumdiv(2*n+1, d, moebius(d)*eulerphi(d)))); j

Crossrefs

Cf. A276833.

Sequence in context: A021970 A115335 A214062 * A214229 A214728 A112752

Adjacent sequences: A054583 A054584 A054585 * A054587 A054588 A054589

Keyword

sign

Author

N. J. A. Sloane, Apr 12 2000

Extensions

Wrong formula deleted by Amiram Eldar, Aug 12 2023

Status

approved