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

1, 14, 69, 102, 123, 134, 164, 276, 639, 2556, 9568, 1259196, 1333334, 1473381, 1741983, 133333334, 821554911, 929247534, 1333333334, 22214600673, 133333333334

Offset: 1

Author

Paolo P. Lava, Jan 22 2015

Keywords

• nonn
• base
• more

Comments

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

a(22) > 10^12. - Giovanni Resta, May 09 2015

Examples

			sigma(14) = 24, Rev(24) = 42 and 42 / 14 = 3.
sigma(69) = 96, Rev(96) = 69 and 69 / 69 = 1.
sigma(9568) = 21168, Rev(21168) = 86112 and 86112 / 9568 = 9.
		

Crossrefs

Cf. A000203, A096507, A007691, A254005.

Programs

Magma

[n: n in [1..10^7] | Seqint(Reverse(Intseq(SumOfDivisors(n)))) mod n eq 0]; // Bruno Berselli, Jan 22 2015

Maple

with(numtheory): T:=proc(w) local x,y,z; x:=w; y:=0;
for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10);
od; y; end:
P:=proc(q) local n; for n from 1 to q do
if type(T(sigma(n))/n,integer) then print(n);
fi; od; end: P(10^9);

Mathematica

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

PARI

isok(n) = !(eval(concat(Vecrev(Str(sigma(n))))) % n); \\ Michel Marcus, Feb 27 2015

Extensions

a(17)-a(20) from Lars Blomberg, Feb 27 2015

a(21) from Giovanni Resta, May 09 2015