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

%I A163838 #9 Jan 23 2021 16:02:52
%S A163838 4,12,16,9,20,48,28,30,48,72,80,42,44,144,25,52,54,112,180,128,66,68,
%T A163838 70,252,76,78,240,252,176,180,92,384,49,200,102,208,324,110,336,114,
%U A163838 116,600,124,252,320,130,396,272,138,420,720,148,300,304,154,468,640,243
%N A163838 a(n) = (n-th composite) * (number of nontrivial divisors of n-th composite).
%C A163838 The trivial divisors of the n-th composite are 1 and the n-th composite.
%F A163838 a(n) = A002808(n)*A144925(n).
%e A163838 a(1) =  4 (= 4*1);
%e A163838 a(2) = 12 (= 6*2);
%e A163838 a(3) = 16 (= 8*2);
%e A163838 a(4) =  9 (= 9*1);
%e A163838 a(5) = 20 (= 10*2);
%e A163838 a(6) = 48 (= 12*4).
%p A163838 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
%t A163838 # (DivisorSigma[0,#]-2)&/@Select[Range[100],CompositeQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 23 2021 *)
%Y A163838 Cf. A002808, A070824, A144925.
%K A163838 nonn
%O A163838 1,1
%A A163838 _Juri-Stepan Gerasimov_, Aug 05 2009, Aug 06 2009
%E A163838 56 replaced with 112, 310 replaced with 320, and 468 inserted by _R. J. Mathar_, Oct 10 2009