A367687 a(n) is the first prime p such that n*p+1 is the product of n primes counted with multiplicity.

2, 7, 17, 47, 79, 9479, 41, 5923, 199, 33461, 2141, 69173177, 11579, 7655281, 20753, 64869017, 233231, 2622816297743, 341477, 14508897313, 8138947, 24565981007, 27445337, 90698401133219401, 313566167, 2552728502809, 229909997, 23451738297083, 948780491, 20677177107714198558766009, 3390080033

Offset: 1

Author

Zak Seidov and Robert Israel, Nov 26 2023

Keywords

• nonn
• look

Examples

			a(3) = 17 because 17 is prime and 3 * 17 + 1 = 52 = 2^2 * 13 is the product of 3 primes, and no smaller prime works.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A001222, A072060.

Programs

Maple

f:= proc(n)
  uses priqueue;
local Q,t,q,i;
  initialize(Q);
  q:= 2;
  while n mod q = 0 do q:= nextprime(q) od:
  insert([-q^n,q,n],Q);
  do
    t:= extract(Q);
    if -t[1]-1 mod n = 0 and isprime((-t[1]-1)/n) then return (-t[1]-1)/n fi;
    q:= nextprime(t[2]);
    while n mod q = 0 do q:= nextprime(q) od;
    for i from 1 to t[3] do
      insert([t[1]*(q/t[2])^i,q,i],Q);
    od
  od;
end proc:
map(f, [$1..40]);

Formula

A001222(n*a(n)+1) = n.