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

József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter I, p. 10, section I.3.1.a (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 *)

Prog

(PARI) a(n) = {my(f = factor(n)); sigma(f) - eulerphi(f) - numdiv(f); } \\ Amiram Eldar, Apr 25 2024

Crossrefs

Cf. A000203, A000010, A000005, A079538, A079539, A100484.

Sequence in context: A290971 A178636 A353276 * A389040 A146076 A157195

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