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a(n) = d0(d1(w)) - d1(d0(w)), where d0()=number of divisors, d1()=sum of divisors.
6

%I #10 Feb 18 2024 08:24:40

%S 0,-1,0,-2,1,-1,1,-3,-2,-1,3,-6,1,1,1,-4,3,-8,3,-4,-1,2,5,-3,-2,1,1,

%T -4,5,-3,3,-6,3,1,3,-9,1,5,1,-3,5,-3,3,0,-4,5,7,-12,0,-8,5,-6,5,1,5,1,

%U 3,5,9,-12,1,5,-4,-6,5,0,3,0,5,0,9,-20,1,1,-6,0,5,1,7,-10,-3,5,9,-16,5,5,9,3,9,-16,3,4,1,8,9,-10,3,-6,0,-9,5,1,5,1,-1

%N a(n) = d0(d1(w)) - d1(d0(w)), where d0()=number of divisors, d1()=sum of divisors.

%t d0[x_] := DivisorSigma[0, x]

%t d1[x_] := DivisorSigma[1, x]

%t Table[ d0[d1[w]] - d1[d0[w] ], {w, 1, 128}]

%Y Cf. A000005, A000203.

%K easy,sign

%O 1,4

%A _Labos Elemer_, Oct 08 2002