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.

30, 42, 330, 462, 681, 772, 824, 890, 989, 2180, 3030, 4242, 4542, 4722, 8074, 9775, 17331, 23980, 33330, 35823, 36213, 43263, 46662, 47324, 55805, 62121, 62421, 65301, 65451, 66441, 66741, 68181, 68331, 68631, 68781, 69171, 71215, 71452, 73565, 74391, 74417, 74572, 74972

Offset

1,1

Comments

Subset of A080716.

The numbers that are not considered here belong to A062687, numbers all of whose divisors are palindromic. - Michel Marcus, Oct 10 2014

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

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (terms 1..57 from R. J. Mathar, 58..1000 from Amiram Eldar)

Example

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

Maple

Rev:=proc(n)
local a, i, k;
i:=convert(n, base, 10); a:=0;
for k from 1 to nops(i) do a:=a*10+i[k]; od;
a;
end:
P:=proc(j)
local h, m, n, ok, p, r, t;
for m from 1 to j  do
  p:=divisors(m); t:=0; ok:=0;
  for r from 1 to nops(p) do t:=t+Rev(p[r]); if p[r]<>Rev(p[r]) then ok:=1; fi;     od;
  if ok=1 and sigma(m)=t then print(m); fi;
od;
end:
P(100000);
# alternative
isA196677 := proc(n)
    isA080716(n) and not isA062687(n) ;
end proc:
n := 1;
for i from 1 do
    if isA196677(i) then
        printf("%d %d\n", n, i) ;
        n := n+1 ;
    end if;
end do: # R. J. Mathar, Sep 09 2015

Prog

(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

Crossrefs

Cf. A000203, A069192, A069942, A080716.

Sequence in context: A268697 A258358 A090692 * A225326 A226727 A102843

Adjacent sequences: A196674 A196675 A196676 * A196678 A196679 A196680

Keyword

nonn,base

Author

Paolo P. Lava, Oct 05 2011

Status

approved