A152992 a(n) = sigma(n) - d(n) - pi(n).

0, 0, 0, 2, 1, 5, 2, 7, 6, 10, 5, 17, 6, 14, 14, 20, 9, 26, 10, 28, 20, 24, 13, 43, 19, 29, 27, 41, 18, 54, 19, 46, 33, 39, 33, 71, 24, 44, 40, 70, 27, 75, 28, 64, 58, 54, 31, 99, 39, 72, 53, 77, 36, 96, 52, 96, 60, 70, 41, 139, 42, 74, 80, 102, 62, 118, 47, 101, 73, 117, 50

Offset: 1

Author

Omar E. Pol, Dec 19 2008, Dec 31 2008

Keywords

• easy
• nonn

Examples

			a(15) = 24 - 4 - 6 = 14 because the sum of divisors of 15 is 1 + 3 + 5 + 15 = 24, the number of divisors of 15 is 4 (1,3,5,15) and the number of primes not exceeding 15 is 6 (2,3,5,7,11,13). - _Emeric Deutsch_, Dec 30 2008
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000203, A000720, A065608, A152770, A152991.

Programs

Maple

with(numtheory): seq(sigma(n)-tau(n)-pi(n), n = 1 .. 75); # Emeric Deutsch, Dec 30 2008

Mathematica

Table[DivisorSigma[1,n]-DivisorSigma[0,n]-PrimePi[n],{n,75}] (* Harvey P. Dale, Sep 19 2011 *)

Formula

a(n) = A000203(n) - A000005(n) - A000720(n) = A065608(n) - A000720(n) = A152991(n) - A000005(n).

Extensions

Corrected and extended by Emeric Deutsch, Dec 30 2008