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A308486 Numbers such that the sum of divisors divides the concatenation (in ascending order) of divisors.

%I A308486 #38 Sep 08 2022 08:46:21
%S A308486 1,2,6,10,40,98,112,120,1904,2680,4040,4128,5136,9920,12224,17900,
%T A308486 20880,27800,44160,55520,57121,62240,86866,158880,178120,1431808,
%U A308486 1773920,1825280,1918640,3751328,5452288,6749600,7262120,7446720,9916832,17777440,46168000,101829808
%N A308486 Numbers such that the sum of divisors divides the concatenation (in ascending order) of divisors.
%C A308486 Numbers k such that A000203(k) divides A037278(k). - _Michel Marcus_, Jun 02 2019.
%C A308486 Similar to A308533 where anti-divisors are considered.
%H A308486 Giovanni Resta, <a href="/A308486/b308486.txt">Table of n, a(n) for n = 1..50</a>
%e A308486 Divisors of 98 are 1, 2, 7, 14, 49, 98 and their sum is sigma(98) = 171. Then, 127144998 / 171 = 743538.
%p A308486 with(numtheory): P:=proc(q) local n; for n from 1 to q do if frac(parse(cat(op(sort([op(divisors(n))]))))/sigma(n))=0 then
%p A308486 print(n); fi; od; end: P(10^6);
%t A308486 Select[Range[10^6], Mod[FromDigits@ Flatten@ IntegerDigits[#], Total@ #] == 0 &@ Divisors@ # &] (* _Michael De Vlieger_, Jun 03 2019 *)
%o A308486 (Magma) k:=1; sol:=[];
%o A308486 for u in [1..10000000] do D:=Divisors(u); conc:=D[1];
%o A308486     for u1 in [2..#D] do a:=#Intseq(conc); a1:=#Intseq(D[u1]); conc:=10^a1*conc+D[u1];
%o A308486     end for;
%o A308486       if conc mod SumOfDivisors(u) eq 0 then sol[k]:=u; k:=k+1; end if;
%o A308486 end for;
%o A308486 sol; // _Marius A. Burtea_, Jun 01 2019
%o A308486 (PARI) concd(n) = my(d=divisors(n), s=""); fordiv(n, d, s = concat(s, Str(d))); eval(s); \\ A037278
%o A308486 isok(n) = (concd(n) % sigma(n)) == 0; \\ _Michel Marcus_, Jun 05 2019
%Y A308486 Cf. A000203, A037278, A069872, A224930, A240265, A308533.
%K A308486 nonn,base
%O A308486 1,2
%A A308486 _Paolo P. Lava_, May 31 2019
%E A308486 a(30)-a(38) from _Giovanni Resta_, May 31 2019