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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.
3

%I #29 Sep 08 2022 08:45:59

%S 30,42,330,462,681,772,824,890,989,2180,3030,4242,4542,4722,8074,9775,

%T 17331,23980,33330,35823,36213,43263,46662,47324,55805,62121,62421,

%U 65301,65451,66441,66741,68181,68331,68631,68781,69171,71215,71452,73565,74391,74417,74572,74972

%N 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 Subset of A080716.

%C The numbers that are not considered here belong to A062687, numbers all of whose divisors are palindromic. - _Michel Marcus_, Oct 10 2014

%C 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 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 Divisors of 989 are 1, 23, 43, 989 and 1+23+43+989=1+32+34+989=1056.

%e 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 Rev:=proc(n)

%p local a,i,k;

%p i:=convert(n,base,10); a:=0;

%p for k from 1 to nops(i) do a:=a*10+i[k]; od;

%p a;

%p end:

%p P:=proc(j)

%p local h,m,n,ok,p,r,t;

%p for m from 1 to j do

%p p:=divisors(m); t:=0; ok:=0;

%p 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 if ok=1 and sigma(m)=t then print(m); fi;

%p od;

%p end:

%p P(100000);

%p # alternative

%p isA196677 := proc(n)

%p isA080716(n) and not isA062687(n) ;

%p end proc:

%p n := 1;

%p for i from 1 do

%p if isA196677(i) then

%p printf("%d %d\n",n,i) ;

%p n := n+1 ;

%p end if;

%p end do: # _R. J. Mathar_, Sep 09 2015

%o (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 Cf. A000203, A069192, A069942, A080716.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Oct 05 2011