A166983 The n-th composite minus the number of its divisors.

1, 2, 4, 6, 6, 6, 10, 11, 11, 12, 14, 17, 18, 16, 22, 22, 23, 22, 22, 26, 29, 30, 31, 27, 34, 35, 32, 34, 38, 39, 42, 38, 46, 44, 47, 46, 46, 51, 48, 53, 54, 48, 58, 57, 57, 61, 58, 62, 65, 62, 60, 70, 69, 70, 73, 70, 70, 76, 78, 72, 81, 82, 83, 80, 78, 87, 86, 89, 90, 91, 84

Offset: 1

Author

Juri-Stepan Gerasimov, Oct 26 2009

Keywords

• nonn

Examples

			a(1)=4-3=1, a(2)=6-4=2, a(3)=8-4=4.
		

Links

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

Crossrefs

Cf. A000005, A002808.

Programs

Mathematica

With[{comps=Rest[Complement[Range[100],Prime[Range[PrimePi[100]]]]]}, #-DivisorSigma[0,#]&/@comps] (* Harvey P. Dale, Dec 16 2011 *)
#-DivisorSigma[0,#]&/@Select[Range[100],CompositeQ] (* Harvey P. Dale, Aug 20 2025 *)

Formula

a(n)=A002808(n)-A000005(A002808(n)) = A002808(n)-A035004(n+1).

Extensions

Formula and two entries corrected by R. J. Mathar, May 21 2010.