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A253824
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Numbers n = concat(s,t) such that n = sigma(s) * sigma(t), where sigma(x) is the sum of the divisors of x.
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9
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540, 2352, 28224, 82890, 737856, 1524096, 1531152, 3429216, 17062920, 22264200, 23268600, 49447728, 104941200, 162496048, 197499456, 267450144, 502334784, 619672032, 2347826040, 2942021520, 4045874976, 4302305280, 9876226752
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OFFSET
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1,1
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LINKS
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EXAMPLE
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540 = concat(5,40) -> sigma(5) = 6, sigma(40) = 90 and 6*90 = 540.
2352 = concat(23,52) -> sigma(23) = 24, sigma(52) = 98 and 24*98 = 2352.
28224 = concat(28,224) -> sigma(28) = 56, sigma(224) = 504 and 56*504 = 28222.
82890 = concat(8,2890) -> sigma(8) = 15, sigma(2890) = 5526 and 15*5526 = 82890.
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MAPLE
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with(numtheory): P:=proc(q) local s, t, k, n;
for n from 1 to q do for k from 1 to ilog10(n) do s:=n mod 10^k; t:=trunc(n/10^k); if s*t>0 then if sigma(s)*sigma(t)=n
then print(n); break; fi; fi; od; od; end: P(10^6);
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MATHEMATICA
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fQ[n_] := Block[{idn = IntegerDigits@ n, lng = Floor@ Log10@ n}, MemberQ[ Table[ DivisorSigma[1, FromDigits@ Take[ idn, {1, i}]] DivisorSigma[1, FromDigits@ Take[ idn, {i + 1, lng + 1}]], {i, lng}], n]]; k = 1; lst = {}; While[k < 1310000001, If[fQ@ k, AppendTo[ lst, k]; Print@ k]; k++] (* Robert G. Wilson v, Jan 19 2015 *)
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PROG
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(PARI) isok(n) = {len = #Str(n); for (k=1, len-1, na = n\10^k; nb = n % 10^k; if (nb && (n == sigma(na)*sigma(nb)), return (1)); ); } \\ Michel Marcus, Jan 15 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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