A378272 The smallest number whose divisor set mod p has p elements with p = prime(n).

2, 6, 40, 84, 990, 936, 5100, 8208, 12420, 48720, 37200, 139860, 196800, 216720, 118440, 648720, 2180640, 1024800, 1857240, 2385600, 2522880, 4180680, 3884400, 9868320, 17599680, 21816000, 16315200, 18874800, 51273600, 34171200, 48646080, 120163680, 110674080

Offset

1,1

Comments

We observe that a(n) == 0 (mod 6) when n>=4.

Links

Table of n, a(n) for n=1..33.

Formula

a(n) = A280171(prime(n)) = A280171(A000040(n)).

Example

a(3) = 40: divisors are {1,2,4,5,8,10,20,40}, mod prime(3)=5 this gives {0,1,2,3,4}.

Maple

a:= proc(n) option remember; local m, p; p:= ithprime(n); for m from p by p
      while nops(map(d-> d mod p, numtheory[divisors](m)))<p do od; m
    end:
seq(a(n), n=1..20);  # Alois P. Heinz, Nov 21 2024

Mathematica

a[n_] := a[n] = For[p = Prime[n]; k = p, True, k += p, If[Union[Mod[Divisors[k], p]] == Range[0, p - 1], Return[k]]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 33}] (* Jean-François Alcover, Jan 27 2025 *)

Prog

(PARI) a(n) = my(k=1, p=prime(n)); while (#Set(apply(x->Mod(x, p), divisors(k))) != p, k++); k; \\ Michel Marcus, Jan 27 2025

Crossrefs

Cf. A000040, A280171.

Sequence in context: A331702 A288491 A212883 * A377855 A336959 A027161

Adjacent sequences: A378269 A378270 A378271 * A378273 A378274 A378275

Keyword

nonn

Author

Michel Lagneau, Nov 21 2024

Extensions

a(16)-a(33) from Alois P. Heinz, Nov 21 2024

Status

approved