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A371034 For n >= 1, a(n) = A004086(n) if A055483(n) = 1, otherwise a(n) = n / A055483(n).

%I A371034 #39 Jul 09 2024 15:49:01
%S A371034 1,1,1,1,1,1,1,1,1,1,1,4,31,41,5,61,71,2,91,10,7,1,32,4,52,13,3,14,92,
%T A371034 10,13,23,1,43,53,4,73,83,13,10,14,7,34,1,5,23,74,4,94,10,17,25,35,6,
%U A371034 1,65,19,85,95,10,16,31,7,32,56,1,76,34,23,10,17,8,37,47
%N A371034 For n >= 1, a(n) = A004086(n) if A055483(n) = 1, otherwise a(n) = n / A055483(n).
%C A371034 Also a(n) = R(n) if (n, R(n)) are coprime, otherwise a(n) = n / GCD(n, R(n)), where R(n) is the digit reversal of n. a(n) = 1 for n from the union of A011557 and A002113 and A001232 and A008918.
%H A371034 Robert Israel, <a href="/A371034/b371034.txt">Table of n, a(n) for n = 1..10000</a>
%F A371034 a(A011557(k)) = 1, k >= 0.
%F A371034 a(A002113(k)) = 1, k >= 2.
%F A371034 a(A001232(k)) = 1, k >= 1.
%F A371034 a(A008918(k)) = 1, k >= 1.
%e A371034 n = 13: A004086(13) = 31, A055483(13) = 1 thus a(13) = 31.
%e A371034 n = 15: A004086(15) = 51, A055483(15) = 3 thus a(15) = 15/3 = 5.
%p A371034 rev:= proc(n) local L,i;
%p A371034   L:= convert(n,base,10);
%p A371034   add(L[-i]*10^(i-1),i=1..nops(L))
%p A371034 end proc:
%p A371034 f:= proc(n) local r,g;
%p A371034   r:= rev(n);
%p A371034   g:= igcd(n,r);
%p A371034   if g = 1 then r else n/g fi
%p A371034 end proc;
%p A371034 map(f, [$1..100]); # _Robert Israel_, Jul 09 2024
%t A371034 a[n_] := Module[{r = IntegerReverse[n], g}, g = GCD[n, r]; If[g == 1, r, n/g]]; Array[a, 100] (* _Amiram Eldar_, Mar 31 2024 *)
%Y A371034 Cf. A001232, A002113, A002275, A004086, A008918, A011557, A055483, A306273.
%K A371034 nonn,base,look
%O A371034 1,12
%A A371034 _Ctibor O. Zizka_, Mar 31 2024