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

1, 2, 6, 12, 66, 30, 210, 390, 1365, 2310, 3990, 10920, 2730, 84630, 53130, 87780, 114114, 760760, 2042040, 1345890, 285285, 1902810, 570570, 1141140, 25571910, 30240210, 2282280, 358888530, 514083570, 413092680, 998887890, 761140380, 1155284130, 3082219140, 8125850460, 11532931410, 17440042620, 8254436190

Offset: 1

Author

Michel Marcus and Juri-Stepan Gerasimov, Jun 27 2025

Keywords

• nonn

Comments

a(1) = A002110(0), a(2) = A002110(1), a(3) = A002110(2), a(6) = A002110(3), a(7) = A002110(4), a(10) = A002110(5), ...?

a(33) onward > 10^9. - Michael S. Branicky, Jun 30 2025

a(44) = 11125544430. - Robert G. Wilson v, Jul 13 2025

Crossrefs

Cf. A002110, A065295, A384237, A384854, A385100.

Programs

Mathematica

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 *)

PARI

f(n) = sumdiv(n, d, Mod(d, n)^d == d); \\ A384237
a(n) = my(k=1); while(f(k)!=n, k++); k;

Extensions

a(28)-a(32) from Michael S. Branicky, Jun 30 2025

a(33)-a(38) from Robert G. Wilson v, Jul 13 2025