A046520 a(n) = (sum of divisors of n) - phi(n) - (number of divisors of n).

-1, 0, 0, 2, 0, 6, 0, 7, 4, 10, 0, 18, 0, 14, 12, 18, 0, 27, 0, 28, 16, 22, 0, 44, 8, 26, 18, 38, 0, 56, 0, 41, 24, 34, 20, 70, 0, 38, 28, 66, 0, 76, 0, 58, 48, 46, 0, 98, 12, 67, 36, 68, 0, 94, 28, 88, 40, 58, 0, 140, 0, 62, 62, 88, 32, 116, 0, 88, 48, 112, 0, 159, 0, 74

Offset

1,4

Comments

Always >= 0 for n >= 2. a(n)=0 if and only if n is prime.

If n is an even semiprime > 4 (A100484), then a(n) = n. - Wesley Ivan Hurt, Dec 25 2013

References

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section I.3.1 (but they have "tau" instead of "sigma").

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).

Formula

a(n) = A000203(n) - A000010(n) - A000005(n).

Maple

with(numtheory); A046520:=n->sigma(n)-phi(n)-tau(n); seq(A046520(n), n=1..100); # Wesley Ivan Hurt, Dec 25 2013

Mathematica

DivisorSigma[1, #] - EulerPhi[#] - DivisorSigma[0, #] & /@ Range[74] (* Jayanta Basu, Jun 27 2013 *)

Crossrefs

Cf. A000203, A000010, A000005, A079538, A079539.

Sequence in context: A290971 A178636 A353276 * A146076 A157195 A019781

Adjacent sequences: A046517 A046518 A046519 * A046521 A046522 A046523

Keyword

sign,easy

Author

N. J. A. Sloane

Extensions

Corrected by Dean Hickerson, Dec 19 2006

Status

approved