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

1,2

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

Links

Table of n, a(n) for n=1..21.

Example

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.

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 *)

Prog

(Magma) [n: n in [1..10^7] | Seqint(Reverse(Intseq(SumOfDivisors(n)))) mod n eq 0]; // Bruno Berselli, Jan 22 2015
(PARI) isok(n) = !(eval(concat(Vecrev(Str(sigma(n))))) % n); \\ Michel Marcus, Feb 27 2015

Crossrefs

Cf. A000203, A096507, A007691, A254005.

Sequence in context: A008529 A075480 A236164 * A238822 A244943 A347673

Adjacent sequences: A254001 A254002 A254003 * A254005 A254006 A254007

Keyword

nonn,base,more

Author

Paolo P. Lava, Jan 22 2015

Extensions

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

a(21) from Giovanni Resta, May 09 2015

Status

approved