cp's OEIS Frontend

A254004 Numbers that divide the reverse of the sum of their divisors.

%I A254004 #30 Sep 08 2022 08:46:11
%S A254004 1,14,69,102,123,134,164,276,639,2556,9568,1259196,1333334,1473381,
%T A254004 1741983,133333334,821554911,929247534,1333333334,22214600673,
%U A254004 133333333334
%N A254004 Numbers that divide the reverse of the sum of their divisors.
%C A254004 Noting 14, 134, 1333334, 133333334, it appears that (4*10^n+2)/3 is a term herein for any n in A096507. - _Hans Havermann_, Jan 24 2015
%C A254004 a(22) > 10^12. - _Giovanni Resta_, May 09 2015
%e A254004 sigma(14) = 24, Rev(24) = 42 and 42 / 14 = 3.
%e A254004 sigma(69) = 96, Rev(96) = 69 and 69 / 69 = 1.
%e A254004 sigma(9568) = 21168, Rev(21168) = 86112 and 86112 / 9568 = 9.
%p A254004 with(numtheory): T:=proc(w) local x,y,z; x:=w; y:=0;
%p A254004 for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10);
%p A254004 od; y; end:
%p A254004 P:=proc(q) local n; for n from 1 to q do
%p A254004 if type(T(sigma(n))/n,integer) then print(n);
%p A254004 fi; od; end: P(10^9);
%t A254004 Select[Range@ 2000000, Mod[FromDigits@ Reverse@ IntegerDigits@ DivisorSigma[1, #], #] == 0 &] (* _Michael De Vlieger_, May 09 2015 *)
%o A254004 (Magma) [n: n in [1..10^7] | Seqint(Reverse(Intseq(SumOfDivisors(n)))) mod n eq 0]; // _Bruno Berselli_, Jan 22 2015
%o A254004 (PARI) isok(n) = !(eval(concat(Vecrev(Str(sigma(n))))) % n); \\ _Michel Marcus_, Feb 27 2015
%Y A254004 Cf. A000203, A096507, A007691, A254005.
%K A254004 nonn,base,more
%O A254004 1,2
%A A254004 _Paolo P. Lava_, Jan 22 2015
%E A254004 a(17)-a(20) from _Lars Blomberg_, Feb 27 2015
%E A254004 a(21) from _Giovanni Resta_, May 09 2015