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A141276 a(n) = A338038(A002808(n)).

%I A141276 #16 Jul 20 2025 09:00:03
%S A141276 4,5,5,5,7,7,9,8,6,7,9,10,13,8,7,15,6,11,10,7,14,19,12,9,21,16,10,12,
%T A141276 15,10,25,9,9,9,20,17,8,16,12,22,31,12,33,12,8,18,16,21,26,14,10,39,
%U A141276 10,23,18,18,11,7,43,14,22,45,32,16,12,20,27,34,49,24,10,11,16,11,22,18,15,55
%N A141276 a(n) = A338038(A002808(n)).
%e A141276 Let k(n) = n-th composite (A002808(n)). Then:
%e A141276 a(4)=5 because k(4) = 9 = 3^2 and 5=3+2;
%e A141276 a(9)=6 because k(9) = 16 = 2^4 and 6=2+4;
%e A141276 a(10)=7 because k(10) = 18 = 2*3^2 and 7=2+3+2.
%p A141276 A141276 := proc(n) local a, ifs, p, c ; if not isprime(n) then a := 0 ; ifs := ifactors(n)[2] ; for p in ifs do a := a + op(1,p) ; if op(2,p) > 1 then a := a+ op(2,p) ; fi; od: printf("%d,",a) ; end if; return ; end: for n from 4 to 200 do A141276(n); end do; # _R. J. Mathar_, Apr 28 2010
%t A141276 a[n_] := Plus @@ First /@ (f = FactorInteger[n]) + Plus @@ Select[Last /@ f, # > 1 &];a/@Select[Range[106], CompositeQ] (* _James C. McMahon_, Jul 19 2025 *)
%Y A141276 Cf. A002808, A338038.
%K A141276 nonn
%O A141276 1,1
%A A141276 _Juri-Stepan Gerasimov_, Aug 08 2008
%E A141276 Entries checked by _R. J. Mathar_, Apr 28 2010
%E A141276 Edited (with clearer definition) by _N. J. A. Sloane_, Jun 15 2021