A368217 a(n) is the first number == 1 (mod n) that is the product of n primes, counted by multiplicity.

2, 9, 28, 81, 176, 15625, 288, 6561, 1792, 137781, 17920, 244140625, 30720, 7971615, 311296, 43046721, 1492992, 3814697265625, 2752512, 3486784401, 38797312, 242137805625, 28311552, 59604644775390625, 184549376, 51684605176023, 2583691264, 63546645708225, 9512681472, 41858774825571336448888891

Offset

1,1

Comments

a(n) is the first number k == 1 (mod n) such that A001222(k) = n.

A053669(n)^n <= a(n) <= A034694(n).

If n is in A007694 then a(n) = A053669(n)^n.

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

a(4) = 81 because 81 == 1 (mod 4) and 81 = 3^4 is the product of 4 primes, counted by multiplicity, and no smaller number works.

Maple

f:= proc(n) uses priqueue; local p, x, Aprimes, v;
    initialize(Aprimes);
    p:= 2;
    while n mod p = 0 do p:= nextprime(p) od:
    insert([-p^n, p, 0], Aprimes);
    do
      v:= extract(Aprimes);
      x:= -v[1];
      if x mod n = 1 then return x fi;
      if v[3] < n then
        insert([v[1], v[2], v[3]+1], Aprimes);
        p:= nextprime(v[2]);
        while n mod p = 0 do p:= nextprime(p) od;
        x:= x * (p/v[2])^(n-v[3]);
        insert([-x, p, v[3]], Aprimes);
      fi;
    od;
end proc:
f(1):= 2:
map(f, [$1..30]);

Crossrefs

Cf. A001222, A007694, A034694, A053669.

Sequence in context: A341507 A058877 A192693 * A360479 A258347 A323957

Adjacent sequences: A368214 A368215 A368216 * A368218 A368219 A368220

Keyword

nonn

Author

Robert Israel, Dec 17 2023

Status

approved