This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A347705 #6 Oct 27 2021 22:23:57
%S A347705 0,1,1,1,1,2,1,3,1,2,1,4,1,2,2,3,1,4,1,4,2,2,1,7,1,2,3,4,1,5,1,7,2,2,
%T A347705 2,7,1,2,2,7,1,5,1,4,4,2,1,12,1,4,2,4,1,7,2,7,2,2,1,11,1,2,4,8,2,5,1,
%U A347705 4,2,5,1,16,1,2,4,4,2,5,1,12,3,2,1,11,2
%N A347705 Number of factorizations of n with reverse-alternating product > 1.
%C A347705 A factorization of n is a weakly increasing sequence of positive integers > 1 with product n.
%C A347705 We define the alternating product of a sequence (y_1,...,y_k) to be Product_i y_i^((-1)^(i-1)). The reverse-alternating product is the alternating product of the reversed sequence.
%F A347705 a(n) = A001055(n) - A347438(n).
%e A347705 The a(n) factorizations for n = 2, 6, 8, 12, 24, 30, 48, 60:
%e A347705 2 6 8 12 24 30 48 60
%e A347705 2*3 2*4 2*6 3*8 5*6 6*8 2*30
%e A347705 2*2*2 3*4 4*6 2*15 2*24 3*20
%e A347705 2*2*3 2*12 3*10 3*16 4*15
%e A347705 2*2*6 2*3*5 4*12 5*12
%e A347705 2*3*4 2*3*8 6*10
%e A347705 2*2*2*3 2*4*6 2*5*6
%e A347705 3*4*4 3*4*5
%e A347705 2*2*12 2*2*15
%e A347705 2*2*2*6 2*3*10
%e A347705 2*2*3*4 2*2*3*5
%e A347705 2*2*2*2*3
%t A347705 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A347705 revaltprod[q_]:=Product[q[[-i]]^(-1)^(i-1),{i,Length[q]}];
%t A347705 Table[Length[Select[facs[n],revaltprod[#]>1&]],{n,100}]
%Y A347705 Positions of 1's are A000430.
%Y A347705 The weak version (>= instead of >) is A001055, non-reverse A347456.
%Y A347705 The non-reverse version is A339890, strict A347447.
%Y A347705 The version for reverse-alternating product 1 is A347438.
%Y A347705 Allowing any integer reciprocal alternating product gives A347439.
%Y A347705 The even-length case is A347440, also the opposite reverse version.
%Y A347705 Allowing any integer rev-alt product gives A347442, non-reverse A347437.
%Y A347705 The version for partitions is A347449, non-reverse A347448.
%Y A347705 A001055 counts factorizations (strict A045778, ordered A074206).
%Y A347705 A038548 counts possible rev-alt products of factorizations, integer A046951.
%Y A347705 A103919 counts partitions by sum and alternating sum, reverse A344612.
%Y A347705 A292886 counts knapsack factorizations, by sum A293627.
%Y A347705 A347707 counts possible integer reverse-alternating products of partitions.
%Y A347705 Cf. A028983, A119620, A339846, A347441, A347443, A347450, A347463, A347466.
%K A347705 nonn
%O A347705 1,6
%A A347705 _Gus Wiseman_, Oct 12 2021