A383489 a(n) is the number of divisors d_i(m) for which a divisor d_j(m) exists such that d_i(m) < d_j(m) < sigma(d_i(m)) where m = A383488(n).

1, 1, 1, 4, 2, 5, 3, 2, 6, 2, 1, 7, 2, 1, 8, 1, 6, 7, 1, 6, 8, 1, 2, 1, 1, 1, 8, 1, 4, 1, 11, 4, 1, 7, 1, 6, 11, 5, 1, 6, 8, 3, 11, 1, 1, 3, 13, 1, 1, 10, 1, 5, 5, 6, 3, 9, 12, 4, 1, 7, 1, 6, 4, 1, 15, 1, 13, 1, 1, 4, 11, 1, 10, 1, 6, 11, 1, 1, 1, 14, 4, 2, 13

Offset: 1

Author

Felix Huber, May 08 2025

Keywords

• nonn

Examples

			The a(4) = 4 divisors d_i(A383488(4)) = d_i(24) are 4, 6, 8 and 12 because sigma(4) = 7 > 6, sigma(6) = 12 > 8, sigma(8) = 15 > 12 and sigma(12) = 28 > 24.
		

Links

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

Crossrefs

Cf. A000203, A002808, A027750, A109042, A383360, A383488.

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;
A383489:=proc(n)
    local a,i,L;
    L:=Divisors(A383488(n));
    a:=0;
    for i to nops(L)-1 do
        if sigma(L[i])>L[i+1] then
            a:=a+1
        fi
    od;
    return a
end proc;
seq(A383489(n),n=1..83);