A383361 -id:A383361 - cp's OEIS frontend

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

Felix Huber, Apr 26 2025

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

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

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

Cf. A027750, A383361, A383362.

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);

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

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

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

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

A383362 a(n) is the number i for which i*d_i = A383360(n), where d_i is i-th smallest divisor d_i of A383360(n).

Original entry on oeis.org

1, 2, 3, 4, 3, 3, 4, 5, 4, 3, 3, 5, 4, 6, 3, 4, 3, 4, 3, 4, 7, 3, 4, 3, 3, 7, 4, 3, 4, 3, 3, 9, 4, 3, 8, 4, 4, 5, 3, 3, 4, 8, 3, 10, 4, 3, 3, 8, 4, 3, 12, 4, 5, 3, 3, 4, 10, 5, 10, 4, 3, 4, 3, 3, 4, 3, 5, 3, 4, 3, 4, 3, 4, 8, 3, 10, 4, 3, 4, 3, 5, 4, 4, 7, 3, 4

Offset: 1

Felix Huber, May 03 2025

			a(8) = 5 because the 5th smallest divisor of A383360(8) = 30 = 5*6 is 6.

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

Cf. A383360, A383361.

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;
A383362:=proc(n)
    local i,M;
    M:=Divisors(A383360(n));
    for i do
        if A383360(n)/i=M[i] then
            return i
        fi
    od;
end proc;
seq(A383360(n),n=1..86);

a(n) = A383360(n)/A383361(n).

a(n) = A383360(n)/A027750(A383360(n),a(n)).

cp's OEIS Frontend

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

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