A254004 - OEIS

%I #30 Sep 08 2022 08:46:11

%S 1,14,69,102,123,134,164,276,639,2556,9568,1259196,1333334,1473381,

%T 1741983,133333334,821554911,929247534,1333333334,22214600673,

%U 133333333334

%N Numbers that divide the reverse of the sum of their divisors.

%C 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 a(22) > 10^12. - _Giovanni Resta_, May 09 2015

%e sigma(14) = 24, Rev(24) = 42 and 42 / 14 = 3.

%e sigma(69) = 96, Rev(96) = 69 and 69 / 69 = 1.

%e sigma(9568) = 21168, Rev(21168) = 86112 and 86112 / 9568 = 9.

%p with(numtheory): T:=proc(w) local x,y,z; x:=w; y:=0;

%p for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10);

%p od; y; end:

%p P:=proc(q) local n; for n from 1 to q do

%p if type(T(sigma(n))/n,integer) then print(n);

%p fi; od; end: P(10^9);

%t Select[Range@ 2000000, Mod[FromDigits@ Reverse@ IntegerDigits@ DivisorSigma[1, #], #] == 0 &] (* _Michael De Vlieger_, May 09 2015 *)

%o (Magma) [n: n in [1..10^7] | Seqint(Reverse(Intseq(SumOfDivisors(n)))) mod n eq 0]; // _Bruno Berselli_, Jan 22 2015

%o (PARI) isok(n) = !(eval(concat(Vecrev(Str(sigma(n))))) % n); \\ _Michel Marcus_, Feb 27 2015

%Y Cf. A000203, A096507, A007691, A254005.

%K nonn,base,more

%O 1,2

%A _Paolo P. Lava_, Jan 22 2015

%E a(17)-a(20) from _Lars Blomberg_, Feb 27 2015

%E a(21) from _Giovanni Resta_, May 09 2015