A163871 The n-th composite plus the sum of its nontrivial divisors.

6, 11, 14, 12, 17, 27, 23, 23, 30, 38, 41, 31, 35, 59, 30, 41, 39, 55, 71, 62, 47, 53, 47, 90, 59, 55, 89, 95, 83, 77, 71, 123, 56, 92, 71, 97, 119, 71, 119, 79, 89, 167, 95, 103, 126, 83, 143, 125, 95, 143, 194, 113, 123, 139, 95, 167, 185, 120, 125, 223, 107, 131, 119, 179

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 06 2009

Keywords

• nonn
• easy

Comments

Trivial divisors of a number are 1 and the number itself, see A048050.

Examples

			a(1) = 4 + 2 =  6;
a(2) = 6 + 5 = 11;
a(3) = 8 + 6 = 14.
		

Links

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

Crossrefs

Cf. A027750.

Programs

Maple

A002808 := proc(n) local resul,i ; i := 1 ; resul := 4 ; while i < n do resul := resul+1 ; while isprime(resul) do resul := resul+1 ; od ; i := i+1 ; od; RETURN(resul) ; end:
A048050 := proc(n) if n <= 3 then 0; else numtheory[sigma](n)-n-1 ; fi; end:
A163871 := proc(n) A002808(n)+A048050(A002808(n)) ; end: seq(A163871(n),n=1..80) ; # R. J. Mathar, Aug 11 2009

Mathematica

#+Total[Most[Rest[Divisors[#]]]]&/@Select[Range[4,200],!PrimeQ[#]&] (* Harvey P. Dale, Oct 28 2013 *)

Formula

a(n) = A002808(n) + A062825(n+1).

Extensions

a(4) corrected by R. J. Mathar, Aug 11 2009