1,1

For 2 <= n <= 4 the straight line has slope -1 and passes through (2, prime(n) - 1) and (prime(n), 1).

For n >= 5 all terms are odd.

Felix Huber, Table of n, a(n) for n = 1..26

a(1) = prime(1) = 2.

a(n) = Product_{i=1..n} prime(i)^(prime(n+1) - prime(i) + 1) for 2 <= n <= 4.

a(5) = 8603960990625 = 3^6*5^5*7^4*11^2*13^1 because (3, 6), (5, 5), (7, 4), (11, 2) and (13, 1) lie on a straight line and no smaller positive integer with 5 distinct prime factors satisfies this condition.

a(9) = 15817621236456464792473857978501394857765124274167495322265625 = 5^10*11^9*17^8*23^7*29^6*41^4*47^3*53^2*59^1 because (5, 10), (11, 9), (17, 8), (23, 7), (29, 6), (41, 4), (47, 3), (53, 2) and (59, 1) lie on a straight line and no smaller positive integer with 9 distinct prime factors satisfies this condition.

A389339:=proc(n)

local a, b, d, i, k, l, m, p, q;

a:=mul(ithprime(i)^(ithprime(n)-ithprime(i)+1), i=1..n);

for k from 2 while mul((ithprime(k)+2*i)^(n-i), i=0..n-1)<a do

p:=ithprime(k);

for d while mul((p+2*d*i)^(n-i), i=0..n-1)<a do

l:=[p];

m:=1;

for q from p+2*d by 2*d while m<n and mul((l[i]^((q+(n-m+1)*2*d-l[i])/(2*d))), i=1..m)*mul((q+2*d*i)^(n-m-i), i=1..n-m+1)<a do

if isprime(q) then

l:=[op(l), q];

m:=m+1

fi

od;

if m=n then

b:=mul(l[i]^((l[n]-l[i])/(2*d)+1), i=1..n);

if b<a then

a:=b

fi

fi

od

od;

return a

end proc;

seq(A389339(n), n=1..10);

Cf. A001221, A048692, A125666, A338425, A373813, A389340.

Sequence in context: A090904 A125295 A222065 * A253788 A252738 A360067

Adjacent sequences: A389336 A389337 A389338 * A389340 A389341 A389342

Felix Huber, Oct 03 2025

approved