cp's OEIS Frontend

A254005 Numbers that divide the reverse of the sum of their aliquot parts.

%I A254005 #30 Sep 08 2022 08:46:11
%S A254005 1,6,2274,44304,229974,498906,4177662,20671542,22999974,41673714,
%T A254005 73687923,403999652,479444901,4158499614,27378395352,209659386726,
%U A254005 216276435966,229999999974,406406685462,922964834547
%N A254005 Numbers that divide the reverse of the sum of their aliquot parts.
%C A254005 Noting 2274, 229974, and 22999974, 23*10^n-26 is a term herein for any n in A253968. - _Hans Havermann_, Jan 24 2015
%C A254005 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
%C A254005 a(21) > 10^12. - _Giovanni Resta_, May 09 2015
%e A254005 sigma(1) - 1 = 0, Rev(0) = 0 and 0 / 1 = 0.
%e A254005 sigma(6) - 6 = 6, Rev(6) = 6 and 6 / 6 = 1.
%e A254005 sigma(2274) - 2274 = 2286, Rev(2286) = 6822 and 6822 / 2274 = 3.
%p A254005 with(numtheory): T:=proc(w) local x,y,z; x:=w; y:=0;
%p A254005 for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10);
%p A254005 od; y; end:
%p A254005 P:=proc(q) local n; for n from 1 to q do
%p A254005 if type(T(sigma(n)-n)/n,integer) then print(n);
%p A254005 fi; od; end: P(10^9);
%t A254005 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 *)
%o A254005 (PARI) rev(n) = subst(Polrev(digits(n)), x, 10);
%o A254005 isok(n) = rev(sigma(n)-n) % n == 0; \\ _Michel Marcus_, Jan 25 2015
%o A254005 (Magma) [n: n in [1..10^7] | Seqint(Reverse(Intseq(SumOfDivisors(n)-n))) mod n eq 0]; // _Vincenzo Librandi_, May 09 2015
%Y A254005 Cf. A000203, A001065, A253968, A254004.
%K A254005 nonn,base,more
%O A254005 1,2
%A A254005 _Paolo P. Lava_, Jan 22 2015
%E A254005 More terms from _Hans Havermann_, Jan 24 2015
%E A254005 a(13) from _Robert G. Wilson v_, Jan 29 2015
%E A254005 a(14)-a(20) from _Giovanni Resta_, May 09 2015