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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).

%I A383489 #11 May 13 2025 23:59:10
%S A383489 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,
%T A383489 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,
%U A383489 1,13,1,1,4,11,1,10,1,6,11,1,1,1,14,4,2,13
%N 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).
%H A383489 Felix Huber, <a href="/A383489/b383489.txt">Table of n, a(n) for n = 1..10000</a>
%e A383489 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.
%p A383489 with(NumberTheory):
%p A383489 A383488:=proc(n)
%p A383489     option remember;
%p A383489     local k,i,L;
%p A383489     if n=1 then
%p A383489         12
%p A383489     else
%p A383489         for k from procname(n-1)+1 do
%p A383489             L:=Divisors(k);
%p A383489             for i to nops(L)-1 do
%p A383489                 if sigma(L[i])>L[i+1] then
%p A383489                     return k
%p A383489                 fi
%p A383489             od
%p A383489         od
%p A383489     fi;
%p A383489 end proc;
%p A383489 A383489:=proc(n)
%p A383489     local a,i,L;
%p A383489     L:=Divisors(A383488(n));
%p A383489     a:=0;
%p A383489     for i to nops(L)-1 do
%p A383489         if sigma(L[i])>L[i+1] then
%p A383489             a:=a+1
%p A383489         fi
%p A383489     od;
%p A383489     return a
%p A383489 end proc;
%p A383489 seq(A383489(n),n=1..83);
%Y A383489 Cf. A000203, A002808, A027750, A109042, A383360, A383488.
%K A383489 nonn
%O A383489 1,4
%A A383489 _Felix Huber_, May 08 2025