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%I #10 Mar 12 2023 04:20:28
%S 1,6,8,15,21,52,58,82,106,118,268,158,356,1264,1296,388,202,214,226,
%T 130,508,524,1936,160,138,298,692,2608,358,3088,288,446,454,466,932,
%U 478,432,348,1792,538,562,578,586,12032,1268,748,20736,1348,694,706,26368,544,758
%N a(n) is the unique number m such that A126168(m) = A361419(n).
%H Amiram Eldar, <a href="/A361420/b361420.txt">Table of n, a(n) for n = 1..10000</a>
%F A126168(a(n)) = A361419(n).
%t f[p_, e_] := Module[{b = IntegerDigits[e, 2]}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; is[1] = 0; is[n_] := Times @@ f @@@ FactorInteger[n] - n;
%t seq[max_] := Module[{v = s = Table[0, {max}], i}, Do[i = is[k] + 1; If[i <= max, v[[i]]++; s[[i]] = k], {k, 1, max^2}]; s[[Position[v, 1] // Flatten]]];
%t seq[500]
%o (PARI) s(n) = {my(f = factor(n), b); prod(i=1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], f[i, 1]^(2^(#b-k)) + 1, 1))) - n; }
%o lista(nmax) = {my(v = w = vector(nmax+1)); for(k=1, nmax^2, i = s(k) + 1; if(i <= nmax+1, v[i] += 1; w[i] = k)); for(i = 1, nmax+1, if(v[i] == 1, print1(w[i], ", "))); }
%Y Cf. A126168, A361419.
%Y Similar sequences: A357313, A357325.
%K nonn
%O 1,2
%A _Amiram Eldar_, Mar 11 2023