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A254005
Numbers that divide the reverse of the sum of their aliquot parts.
2
1, 6, 2274, 44304, 229974, 498906, 4177662, 20671542, 22999974, 41673714, 73687923, 403999652, 479444901, 4158499614, 27378395352, 209659386726, 216276435966, 229999999974, 406406685462, 922964834547
OFFSET
1,2
COMMENTS
Noting 2274, 229974, and 22999974, 23*10^n-26 is a term herein for any n in A253968. - Hans Havermann, Jan 24 2015
Additionally, 404*10^(6*n)-348 is a term herein if this is 28 times a prime. Three such numbers are known: n = 1, 10, and 1608. - Hans Havermann, Jan 28 2015
a(21) > 10^12. - Giovanni Resta, May 09 2015
EXAMPLE
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.
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 *)
PROG
(PARI) rev(n) = subst(Polrev(digits(n)), x, 10);
isok(n) = rev(sigma(n)-n) % n == 0; \\ Michel Marcus, Jan 25 2015
(Magma) [n: n in [1..10^7] | Seqint(Reverse(Intseq(SumOfDivisors(n)-n))) mod n eq 0]; // Vincenzo Librandi, May 09 2015
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Paolo P. Lava, Jan 22 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
STATUS
approved