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A308486
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Numbers such that the sum of divisors divides the concatenation (in ascending order) of divisors.
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2
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1, 2, 6, 10, 40, 98, 112, 120, 1904, 2680, 4040, 4128, 5136, 9920, 12224, 17900, 20880, 27800, 44160, 55520, 57121, 62240, 86866, 158880, 178120, 1431808, 1773920, 1825280, 1918640, 3751328, 5452288, 6749600, 7262120, 7446720, 9916832, 17777440, 46168000, 101829808
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OFFSET
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1,2
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COMMENTS
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Similar to A308533 where anti-divisors are considered.
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LINKS
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EXAMPLE
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Divisors of 98 are 1, 2, 7, 14, 49, 98 and their sum is sigma(98) = 171. Then, 127144998 / 171 = 743538.
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MAPLE
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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
print(n); fi; od; end: P(10^6);
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MATHEMATICA
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Select[Range[10^6], Mod[FromDigits@ Flatten@ IntegerDigits[#], Total@ #] == 0 &@ Divisors@ # &] (* Michael De Vlieger, Jun 03 2019 *)
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PROG
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(Magma) k:=1; sol:=[];
for u in [1..10000000] do D:=Divisors(u); conc:=D[1];
for u1 in [2..#D] do a:=#Intseq(conc); a1:=#Intseq(D[u1]); conc:=10^a1*conc+D[u1];
end for;
if conc mod SumOfDivisors(u) eq 0 then sol[k]:=u; k:=k+1; end if;
end for;
(PARI) concd(n) = my(d=divisors(n), s=""); fordiv(n, d, s = concat(s, Str(d))); eval(s); \\ A037278
isok(n) = (concd(n) % sigma(n)) == 0; \\ Michel Marcus, Jun 05 2019
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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