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A254004
Numbers that divide the reverse of the sum of their divisors.
1
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
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
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