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A385391 a(n) is the smallest integer k such that A384237(k) = n.

%I A385391 #29 Jul 14 2025 10:04:14
%S A385391 1,2,6,12,66,30,210,390,1365,2310,3990,10920,2730,84630,53130,87780,
%T A385391 114114,760760,2042040,1345890,285285,1902810,570570,1141140,25571910,
%U A385391 30240210,2282280,358888530,514083570,413092680,998887890,761140380,1155284130,3082219140,8125850460,11532931410,17440042620,8254436190
%N A385391 a(n) is the smallest integer k such that A384237(k) = n.
%C A385391 a(1) = A002110(0), a(2) = A002110(1), a(3) = A002110(2), a(6) = A002110(3), a(7) = A002110(4), a(10) = A002110(5), ...?
%C A385391 a(33) onward > 10^9. - _Michael S. Branicky_, Jun 30 2025
%C A385391 a(44) = 11125544430. - _Robert G. Wilson v_, Jul 13 2025
%t A385391 f[n_] := 1 + Total[ Boole[ PowerMod[#, #, n] == # & /@ Divisors[n]]]; k = 3; t[_] := 0; t[1] = 1; t[2] = 2; While[k < 3000000001, a = f@k; If[ t[a] == 0, t[a] = k]; k +=3]; t /@ Range@ 38 (* _Robert G. Wilson v_, Jul 13 2025 *)
%o A385391 (PARI) f(n) = sumdiv(n, d, Mod(d, n)^d == d); \\ A384237
%o A385391 a(n) = my(k=1); while(f(k)!=n, k++); k;
%Y A385391 Cf. A002110, A065295, A384237, A384854, A385100.
%K A385391 nonn
%O A385391 1,2
%A A385391 _Michel Marcus_ and _Juri-Stepan Gerasimov_, Jun 27 2025
%E A385391 a(28)-a(32) from _Michael S. Branicky_, Jun 30 2025
%E A385391 a(33)-a(38) from _Robert G. Wilson v_, Jul 13 2025