A395271 a(n) is the smallest abundant number with radical A395270(n).

12, 20, 56, 88, 104, 30, 272, 304, 42, 368, 464, 992, 66, 70, 1184, 78, 1312, 1376, 1504, 102, 945, 1696, 220, 114, 1888, 1952, 260, 4288, 138, 4544, 4672, 308, 5056, 7425, 5312, 340, 174, 5696, 364, 186, 380, 6208, 131625, 6464, 6592, 210, 6848, 6976, 222, 7232

Offset

1,1

Comments

Nonprimitive terms can occur only for radicals of the form 2*q, where q is an odd prime.

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Example

a(1) = 12, since A395270(1) = 6 and 12 is the smallest abundant number with radical 6.
a(3) = 56, since A395270(3) = 14 and 56 is the smallest abundant number with radical 14.
a(21) = 945, since A395270(21) = 105 = 3*5*7 and 945 is the smallest abundant number with radical 105.

Maple

b := proc(l)
    local c, f, i, m, p, r, x;
    p := sort(l); r := nops(p);
    f := (q, e) -> (q^(e + 1) - 1)/(q^e*(q - 1));
    x := mul(p[i]/(p[i] - 1), i = 1 .. r);
    m := [seq(max(1, ceil(log(1/(1 - 2/x))/log(p[i]))), i = 1 .. r)];
    c := proc(k, u, v, g)
        local e, i, t, w;
        if k > r then if u > 2 then return v else return infinity end if end if;
        t := g;
        for e to m[k] do
            w := v*p[k]^e;
            if w >= t then break end if;
            i := c(k + 1, u*f(p[k], e), w, t);
            if i < t then t := i end if;
        end do;
        t;
    end proc;
    c(1, 1, 1, infinity)
end proc:
A395271 := proc(n) option remember;
    global t; local r;
    r := A395270(n);
    b(t[r]);
end proc:
seq(A395271(n), n = 1 .. 50);

Crossrefs

Cf. A000203, A001221, A005101, A006038, A007947, A091191, A100484, A395270.

Sequence in context: A229355 A259174 A109788 * A341361 A181701 A025104

Adjacent sequences: A395268 A395269 A395270 * A395272 A395273 A395274

Keyword

nonn,easy

Author

Felix Huber, May 12 2026

Status

approved