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%I A322036 #24 Jun 12 2022 15:16:15
%S A322036 1,1,2,1,4,1,6,1,5,2,10,1,12,3,3,1,16,5,18,1,13,5,22,1,19,6,14,3,28,3,
%T A322036 30,1,7,8,27,5,36,9,25,1,40,13,42,5,8,11,46,1,41,19,11,3,52,7,43,3,37,
%U A322036 14,58,3,60,15,34,1,51,7,66,4,15,27,70
%N A322036 a(n) = A322035(n) - A322034(n).
%C A322036 Let s be the fraction defined in A322034 and A322035. Then for n >= 2, 1-s is a(n)/A322035(n).
%C A322036 Note that a(n) >= 1, see A322034.
%H A322036 Seiichi Manyama, <a href="/A322036/b322036.txt">Table of n, a(n) for n = 1..16384</a>
%e A322036 Let s be the fraction defined in A322034 and A322035. The fractions 1-s for n >= 2 are 1/2, 2/3, 1/4, 4/5, 1/3, 6/7, 1/8, 5/9, 2/5, 10/11, 1/6, 12/13, 3/7, 3/5, 1/16, 16/17, 5/18, 18/19, 1/5, 13/21, 5/11, 22/23, 1/12, 19/25, 6/13, 14/27, ...
%p A322036 # This generates the terms starting at n=2:
%p A322036 P:=proc(n) local FM: FM:=ifactors(n)[2]: seq(seq(FM[j][1], k=1..FM[j][2]), j=1..nops(FM)) end: # A027746
%p A322036 f0:=[]; f1:=[]; f2:=[];
%p A322036 for n from 2 to 120 do
%p A322036 a:=0; b:=1; t1:=[P(n)];
%p A322036 for i from 1 to nops(t1) do b:=b/t1[i]; a:=a+b; od;
%p A322036 f0:=[op(f0),a]; f1:=[op(f1), numer(a)]; f2:=[op(f2),denom(a)]; od:
%p A322036 f0;    # s
%p A322036 f1;    # A322034
%p A322036 f2;    # A322035
%p A322036 f2-f1; # A322036
%Y A322036 Cf. A006022, A027746, A322034, A322035.
%K A322036 nonn,frac
%O A322036 1,3
%A A322036 _N. J. A. Sloane_ and _David James Sycamore_, Nov 28 2018

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