cp's OEIS Frontend

A243982 Number of divisors of n minus the number of parts in the symmetric representation of sigma(n).

%I A243982 #30 Aug 11 2025 22:09:49
%S A243982 0,1,0,2,0,3,0,3,0,2,0,5,0,2,1,4,0,5,0,5,0,2,0,7,0,2,0,5,0,7,0,5,0,2,
%T A243982 1,8,0,2,0,7,0,7,0,4,3,2,0,9,0,3,0,4,0,7,0,7,0,2,0,11,0,2,1,6,0,7,0,4,
%U A243982 0,5,0,11,0,2,2,4,1,6,0,9,0,2,0,11,0,2,0,7,0,11,1,4,0,2,0,11,0,3,1,8,0,6,0,7
%N A243982 Number of divisors of n minus the number of parts in the symmetric representation of sigma(n).
%C A243982 Conjecture: a(n) is the number of divisors r of n such that r is not greater than twice the adjacent previous divisor of n. - _Omar E. Pol_, Aug 04 2025
%H A243982 Antti Karttunen, <a href="/A243982/b243982.txt">Table of n, a(n) for n = 1..5000</a> (computed from the b-file of A237271 provided by Michel Marcus)
%F A243982 a(n) = A000005(n) - A237271(n).
%e A243982 For n = 9 the divisors of 9 are [1, 3, 9] and the parts of the symmetric representation of sigma(9) are [5, 3, 5]. In both cases there are three elements, so a(9) = 3 - 3 = 0.
%e A243982 For n = 10 the four divisors of 10 are [1, 2, 5, 10] and the two parts of the symmetric representation of sigma(10) are [9, 9], so a(10) = 4 - 2 = 2.
%t A243982 (* Function a237270[] is defined in A237270 *)
%t A243982 a243982[n_]:=Length[Divisors[n] - Length[a237270[n]]
%t A243982 a243982[m_, n_]:=Map[a243982, Range[m,n]]
%t A243982 a243982[1, 104]] (* data *)
%t A243982 (* _Hartmut F. W. Hoft_, Sep 19 2014 *)
%Y A243982 Cf. A000005, A000203, A071561, A071562, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239657, A239660, A239931-A239934.
%K A243982 nonn
%O A243982 1,4
%A A243982 _Omar E. Pol_, Jun 16 2014
%E A243982 a(94)-a(95) corrected by _Omar E. Pol_, Jul 02 2014