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a(n) is the number of solutions k to A075254(k) = n.
2

%I #10 Jul 15 2021 18:54:22

%S 1,0,0,1,0,1,0,1,0,1,1,0,0,2,1,0,1,0,1,0,0,1,2,1,0,2,0,0,1,0,1,0,1,1,

%T 2,1,0,1,1,1,1,1,0,0,0,2,2,0,0,0,1,0,1,1,1,1,0,1,3,0,0,2,1,0,1,0,0,0,

%U 2,0,3,1,0,1,0,2,0,0,1,0,0,2,1,2,0,1,0,1,2,0,0,0,2,1,3,1,0,1,1

%N a(n) is the number of solutions k to A075254(k) = n.

%C a(n) is the number of k such that k + A001414(k) = n.

%H Robert Israel, <a href="/A346377/b346377.txt">Table of n, a(n) for n = 1..10000</a>

%e a(14) = 2 because there are two solutions to A075254(k) = 14, namely

%e A075254(7) = 7+7 = 14

%e A075254(8) = 8+2+2+2 = 14

%p f:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2])+n end proc:

%p N:= 100: # for a(1)..a(N)

%p V:= Vector(N):

%p for n from 1 to N do

%p v:= f(n);

%p if v <= N then V[v]:= V[v]+1 fi

%p od:

%p convert(V[1..N],list);

%t f[1] = 1; f[n_] := n + Plus @@ Times @@@ FactorInteger[n]; m = 100; v = Table[0, {m}]; Do[i = f[n]; If[i <= m, v[[i]]++], {n, 1, m}]; v (* _Amiram Eldar_, Jul 14 2021 *)

%Y Cf. A001414, A075254, A346378.

%K nonn

%O 1,14

%A _J. M. Bergot_ and _Robert Israel_, Jul 14 2021