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%I A196677 #29 Sep 08 2022 08:45:59
%S A196677 30,42,330,462,681,772,824,890,989,2180,3030,4242,4542,4722,8074,9775,
%T A196677 17331,23980,33330,35823,36213,43263,46662,47324,55805,62121,62421,
%U A196677 65301,65451,66441,66741,68181,68331,68631,68781,69171,71215,71452,73565,74391,74417,74572,74972
%N A196677 Numbers n such that sum of the divisors of n equals the sum of the reversals of the divisors of n. Numbers with all palindrome divisors are not in the sequence.
%C A196677 Subset of A080716.
%C A196677 The numbers that are not considered here belong to A062687, numbers all of whose divisors are palindromic. - _Michel Marcus_, Oct 10 2014
%C A196677 The sequence contains the terms palindromic numbers: 989, 97079, 98789, 99299, 1226221, 1794971, 13488431,…. Divisors(97079) = {1, 193, 503, 97079} and 193 + 503 = 696 = 391 + 305. Divisors(1794971) = {1, 1031, 1741, 1794971} and 1031 + 1741 = 2772 = 1301 + 1471. - _Marius A. Burtea_, Nov 20 2019
%H A196677 Giovanni Resta, <a href="/A196677/b196677.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..57 from R. J. Mathar, 58..1000 from Amiram Eldar)
%e A196677 Divisors of 989 are 1, 23, 43, 989 and 1+23+43+989=1+32+34+989=1056.
%e A196677 Divisors of 8074 are 1, 2, 11, 22, 367, 734, 4037, 8074 and 1+2+11+22+367+734+4037+8074=1+2+11+22+763+437+7304+4708=13248.
%p A196677 Rev:=proc(n)
%p A196677 local a,i,k;
%p A196677 i:=convert(n,base,10); a:=0;
%p A196677 for k from 1 to nops(i) do a:=a*10+i[k]; od;
%p A196677 a;
%p A196677 end:
%p A196677 P:=proc(j)
%p A196677 local h,m,n,ok,p,r,t;
%p A196677 for m from 1 to j  do
%p A196677   p:=divisors(m); t:=0; ok:=0;
%p A196677   for r from 1 to nops(p) do t:=t+Rev(p[r]); if p[r]<>Rev(p[r]) then ok:=1; fi;     od;
%p A196677   if ok=1 and sigma(m)=t then print(m); fi;
%p A196677 od;
%p A196677 end:
%p A196677 P(100000);
%p A196677 # alternative
%p A196677 isA196677 := proc(n)
%p A196677     isA080716(n) and not isA062687(n) ;
%p A196677 end proc:
%p A196677 n := 1;
%p A196677 for i from 1 do
%p A196677     if isA196677(i) then
%p A196677         printf("%d %d\n",n,i) ;
%p A196677         n := n+1 ;
%p A196677     end if;
%p A196677 end do: # _R. J. Mathar_, Sep 09 2015
%o A196677 (Magma) f:=func<n|Intseq(n) eq Reverse(Intseq(n))>; g:=func<n|[&+Divisors(n)] eq [&+[Seqint(Reverse(Intseq(d))):d in Divisors(n)]]>; [k:k in [1..80000]| g(k) and not forall{d:d in Divisors(k)|f(d)}]; // _Marius A. Burtea_, Nov 20 2019
%Y A196677 Cf. A000203, A069192, A069942, A080716.
%K A196677 nonn,base
%O A196677 1,1
%A A196677 _Paolo P. Lava_, Oct 05 2011

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