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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)).

%I A383488 #8 May 08 2025 21:06:15
%S A383488 12,18,20,24,30,36,40,42,48,54,56,60,66,70,72,78,80,84,88,90,96,99,
%T A383488 100,102,104,105,108,110,112,114,120,126,130,132,138,140,144,150,154,
%U A383488 156,160,162,168,170,174,176,180,186,189,192,196,198,200,204,208,210,216
%N 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)).
%C A383488 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].
%H A383488 Felix Huber, <a href="/A383488/b383488.txt">Table of n, a(n) for n = 1..10000</a>
%e A383488 All multiples of 12 (A008594) are terms because 12 has the divisors 4 and 6 where sigma(4) = 7 > 6.
%e A383488 All multiples of 18 (A008600) are terms because 18 has the divisors 6 and 9 where sigma(6) = 12 > 9.
%e A383488 All multiples of 20 (A008602) are terms because 20 has the divisors 4 and 5 where sigma(4) = 7 > 5.
%p A383488 with(NumberTheory):
%p A383488 A383488:=proc(n)
%p A383488     option remember;
%p A383488     local k,i,L;
%p A383488     if n=1 then
%p A383488         12
%p A383488     else
%p A383488         for k from procname(n-1)+1 do
%p A383488             L:=Divisors(k);
%p A383488             for i to nops(L)-1 do
%p A383488                 if sigma(L[i])>L[i+1] then
%p A383488                     return k
%p A383488                 fi
%p A383488             od
%p A383488         od
%p A383488     fi;
%p A383488 end proc;
%p A383488 seq(A383488(n),n=1..57);
%Y A383488 Supersequence of A008594, A008600, A008602, A008606, A044102, A135628.
%Y A383488 Cf. A000203, A002808, A027750, A109042, A383360, A383489.
%K A383488 nonn
%O A383488 1,1
%A A383488 _Felix Huber_, May 03 2025