A383360 Numbers k that have an i-th smallest divisor d_i(k) for which i*d_i(k) = k.

1, 4, 15, 20, 21, 27, 28, 30, 32, 33, 39, 40, 44, 48, 51, 52, 57, 68, 69, 76, 84, 87, 92, 93, 111, 112, 116, 123, 124, 129, 141, 144, 148, 159, 160, 164, 172, 175, 177, 183, 188, 200, 201, 210, 212, 213, 219, 224, 236, 237, 240, 244, 245, 249, 267, 268, 270, 275

Offset: 1

Author

Felix Huber, Apr 26 2025

Keywords

• nonn
• easy

Comments

Numbers k for which a number i exists such that k = i*A027750(k,i).

Examples

			30 is in the sequence because its 5th smallest divisor is 6 and 5*6 = 30.
		

Links

• Felix Huber, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Divisor.

Crossrefs

Cf. A027750, A383361, A383362.

Programs

Maple

with(NumberTheory):
A383360:=proc(n)
    option remember;
    local k,i,L;
    if n=1 then
        1
    else
        for k from procname(n-1)+1 do
            L:=Divisors(k);
            for i to tau(k) do
                if L[i]*i=k then
                    return k
                fi
            od
        od
    fi;
end proc;
seq(A383360(n),n=1..58);

Mathematica

q[k_] := AnyTrue[(d = Divisors[k]) * Range[Length[d]], # == k &]; Select[Range[300], q] (* Amiram Eldar, Apr 26 2025 *)

PARI

isok(k) = my(d=divisors(k)); for (i=1, #d, if (d[i]*i == k, return(1))); \\ Michel Marcus, Apr 26 2025

Formula

a(n) = A383362(n)*A383361(n).

a(n) = A383362(n)*A027750(a(n),A383362(n)).