A163838 a(n) = (n-th composite) * (number of nontrivial divisors of n-th composite).

4, 12, 16, 9, 20, 48, 28, 30, 48, 72, 80, 42, 44, 144, 25, 52, 54, 112, 180, 128, 66, 68, 70, 252, 76, 78, 240, 252, 176, 180, 92, 384, 49, 200, 102, 208, 324, 110, 336, 114, 116, 600, 124, 252, 320, 130, 396, 272, 138, 420, 720, 148, 300, 304, 154, 468, 640, 243

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 05 2009, Aug 06 2009

Keywords

• nonn

Comments

The trivial divisors of the n-th composite are 1 and the n-th composite.

Examples

			a(1) =  4 (= 4*1);
a(2) = 12 (= 6*2);
a(3) = 16 (= 8*2);
a(4) =  9 (= 9*1);
a(5) = 20 (= 10*2);
a(6) = 48 (= 12*4).
		

Crossrefs

Cf. A002808, A070824, A144925.

Programs

Maple

A002808 := proc(n) option remember; local a; if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then return a; end if; end do: end if; end proc: A070824 := proc(n) numtheory[tau](n)-2 ; end: A144925 := proc(n) A070824(A002808(n)) ; end: A163838 := proc(n) A144925(n)*A002808(n) ; end: seq(A163838(n),n=1..80) ; # R. J. Mathar, Oct 10 2009

Mathematica

# (DivisorSigma[0,#]-2)&/@Select[Range[100],CompositeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 23 2021 *)

Formula

a(n) = A002808(n)*A144925(n).

Extensions

56 replaced with 112, 310 replaced with 320, and 468 inserted by R. J. Mathar, Oct 10 2009