A368217 - OEIS

%I #12 Dec 18 2023 12:22:12

%S 2,9,28,81,176,15625,288,6561,1792,137781,17920,244140625,30720,

%T 7971615,311296,43046721,1492992,3814697265625,2752512,3486784401,

%U 38797312,242137805625,28311552,59604644775390625,184549376,51684605176023,2583691264,63546645708225,9512681472,41858774825571336448888891

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

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

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

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

%H Robert Israel, <a href="/A368217/b368217.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%p f:= proc(n) uses priqueue; local p, x, Aprimes, v;

%p     initialize(Aprimes);

%p     p:= 2;

%p     while n mod p = 0 do p:= nextprime(p) od:

%p     insert([-p^n,p,0],Aprimes);

%p     do

%p       v:= extract(Aprimes);

%p       x:= -v[1];

%p       if x mod n = 1 then return x fi;

%p       if v[3] < n then

%p         insert([v[1],v[2],v[3]+1],Aprimes);

%p         p:= nextprime(v[2]);

%p         while n mod p = 0 do p:= nextprime(p) od;

%p         x:= x * (p/v[2])^(n-v[3]);

%p         insert([-x,p,v[3]],Aprimes);

%p       fi;

%p     od;

%p end proc:

%p f(1):= 2:

%p map(f, [$1..30]);

%Y Cf. A001222, A007694, A034694, A053669.

%K nonn

%O 1,1

%A _Robert Israel_, Dec 17 2023