A078119 a(n) = sigma(n) - phi(n+2), where sigma = sum of divisors (A000203) and phi = Euler totient function (A000010).

-1, 1, 0, 5, 0, 8, 2, 11, 3, 14, 0, 22, 6, 16, 8, 25, 0, 31, 8, 32, 10, 28, 4, 48, 13, 30, 12, 48, 0, 56, 12, 47, 24, 42, 12, 73, 14, 44, 16, 78, 0, 76, 20, 62, 32, 56, 6, 104, 25, 69, 20, 80, 14, 96, 36, 92, 22, 74, 0, 138, 26, 64, 56, 107, 18, 112, 24, 102, 26, 120, 0, 159, 34, 78, 64, 116, 18

Offset

1,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

For n>1: a(n) >= 0 and a(n) = 0 iff (n,n+2) is a twin prime pair.

Sum_{k=1..n} a(k) ~ c * n^2 + O(n*log(n)), where c = Pi^2/12 - 3/Pi^2 = 0.518503... . - Amiram Eldar, Apr 15 2025

Mathematica

Table[DivisorSigma[1, n]-EulerPhi[n+2], {n, 80}] (* Harvey P. Dale, Dec 25 2012 *)

Prog

(PARI) a(n)=sigma(n)-eulerphi(n+2) \\ Charles R Greathouse IV, Feb 19 2013

Crossrefs

Cf. A000010, A000203, A001359, A006512.

Sequence in context: A011510 A394174 A021667 * A085998 A094886 A371506

Adjacent sequences: A078116 A078117 A078118 * A078120 A078121 A078122

Keyword

sign

Author

Reinhard Zumkeller, Dec 06 2002

Status

approved