A383488 Numbers k that have at least one divisor d_i(k) for which a divisor d_j(k) exists such that d_i(k) < d_j(k) < sigma(d_i(k)).

12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 99, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 130, 132, 138, 140, 144, 150, 154, 156, 160, 162, 168, 170, 174, 176, 180, 186, 189, 192, 196, 198, 200, 204, 208, 210, 216

Offset: 1

Author

Felix Huber, May 03 2025

Keywords

• nonn

Comments

Numbers k (without multiplicity) that are multiples of lcm(c,i), where c is any composite and i is any integer from [c + 1, sigma(c) - 1].

Examples

			All multiples of 12 (A008594) are terms because 12 has the divisors 4 and 6 where sigma(4) = 7 > 6.
All multiples of 18 (A008600) are terms because 18 has the divisors 6 and 9 where sigma(6) = 12 > 9.
All multiples of 20 (A008602) are terms because 20 has the divisors 4 and 5 where sigma(4) = 7 > 5.
		

Links

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

Crossrefs

Supersequence of A008594, A008600, A008602, A008606, A044102, A135628.

Cf. A000203, A002808, A027750, A109042, A383360, A383489.

Programs

Maple

with(NumberTheory):
A383488:=proc(n)
    option remember;
    local k,i,L;
    if n=1 then
        12
    else
        for k from procname(n-1)+1 do
            L:=Divisors(k);
            for i to nops(L)-1 do
                if sigma(L[i])>L[i+1] then
                    return k
                fi
            od
        od
    fi;
end proc;
seq(A383488(n),n=1..57);