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A254005
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Numbers that divide the reverse of the sum of their aliquot parts.
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2
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1, 6, 2274, 44304, 229974, 498906, 4177662, 20671542, 22999974, 41673714, 73687923, 403999652, 479444901, 4158499614, 27378395352, 209659386726, 216276435966, 229999999974, 406406685462, 922964834547
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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MAPLE
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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);
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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