A254005 Numbers that divide the reverse of the sum of their aliquot parts.
1, 6, 2274, 44304, 229974, 498906, 4177662, 20671542, 22999974, 41673714, 73687923, 403999652, 479444901, 4158499614, 27378395352, 209659386726, 216276435966, 229999999974, 406406685462, 922964834547
Offset: 1
Examples
sigma(1) - 1 = 0, Rev(0) = 0 and 0 / 1 = 0. sigma(6) - 6 = 6, Rev(6) = 6 and 6 / 6 = 1. sigma(2274) - 2274 = 2286, Rev(2286) = 6822 and 6822 / 2274 = 3.
Programs
-
Magma
[n: n in [1..10^7] | Seqint(Reverse(Intseq(SumOfDivisors(n)-n))) mod n eq 0]; // Vincenzo Librandi, May 09 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)/n,integer) then print(n); fi; od; end: P(10^9);
-
Mathematica
fQ[n_] := Mod[ FromDigits@ Reverse@ IntegerDigits[ DivisorSigma[1, n] - n], n] == 0; k = 1; lst = {}; While[k < 1000000001, If[fQ@ k, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Jan 28 2015 *) -
PARI
rev(n) = subst(Polrev(digits(n)), x, 10); isok(n) = rev(sigma(n)-n) % n == 0; \\ Michel Marcus, Jan 25 2015
Extensions
More terms from Hans Havermann, Jan 24 2015
a(13) from Robert G. Wilson v, Jan 29 2015
a(14)-a(20) from Giovanni Resta, May 09 2015
Comments