A392045 - OEIS

%I #8 Jan 08 2026 23:14:53

%S 9,81,625,2025,5625,15625,117649,455625,1265625,5764801,22325625,

%T 37515625,43758225,62015625,73530625,238239225,337640625,661775625,

%U 25937424601,45956640625,90075015625,246140015625,482434430625,683722265625,2626587455625,3138428376721

%N Odd positive integers whose canonical prime factorization p_1^e_1*...*p_r^e_r satisfies that {p_1, ..., p_r, e_1, ..., e_r} is a set of 2*r consecutive integers.

%C For r = 1, p_1 is an odd prime. For r > 1, p_(i+1) = p_i + 2. Every permutation of even numbers in [p_1 - 1; p_r - 1] and in [p_1 + 1; p_r + 1] gives a set of exponents e_i.

%H Felix Huber, <a href="/A392045/b392045.txt">Table of n, a(n) for n = 1..222</a>

%e 2025 = 3^4*5^2 is a term since 2025 is odd and 2, 3, 4, 5 are consecutive integers.

%e 22325625 = 3^6*5^4*7^2 is a term since 22325625 is odd and 2, 3, 4, 5, 6, 7 are consecutive integers.

%p with(combinat):

%p A392045List := proc(N)

%p     local a, b, e, f, i, j, k, l, m, p, q;

%p     a := [];

%p     for i from 2 do

%p         b := [];

%p         q := ithprime(i);

%p         p := [];

%p         while isprime(q) do

%p             p := [op(p), q];

%p             q := q + 2;

%p         od;

%p         l := nops(p);

%p         for j to l do

%p             e := permute([seq(2*k, k = (p[1] - 1)/2 ... (p[j] - 1)/2)]);

%p             f := permute([seq(2*k, k = (p[1] + 1)/2 ... (p[j] + 1)/2)]);

%p             for m to nops(e) do

%p                 b := [op(b), op(select(x -> x <= N, [mul(p[k]^e[m, k], k = 1 .. j), mul(p[k]^f[m, k], k = 1 .. j)]))];

%p             od

%p         od;

%p         if b = [] then

%p             break

%p         else

%p             a := [op(a), op(b)]

%p         fi

%p     od;

%p     sort(a)

%p end proc:

%p A392045List(3138428376721);

%Y Cf. A111774, A382330, A390784, A392046, A392047.

%Y Cf. A097320, A383397, A387172, A387586, A389339, A389340, A389795.

%K nonn,easy

%O 1,1

%A _Felix Huber_, Jan 05 2026