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A260097
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Numbers n = concat(s,t) such that n = sigma(s*t), where sigma(x) is the sum of the divisors of x.
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0
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124, 2352, 2604, 6804, 15240, 63180, 225302, 632400, 1531152, 2537040, 4592588, 7160400, 7603680, 26100144, 26378352, 31492032, 33747840, 49447728, 88385040, 104941200, 162496048, 175600040, 197499456, 403242624, 483741216, 797091840, 2077442640, 2942021520, 4045874976, 4828299840
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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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124 = concat(12,4) and sigma(12*4) = sigma(48) = 124.
2352 = concat(23,52) and sigma(23*52) = sigma(1196) = 2352.
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MAPLE
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with(numtheory); P:=proc(q) local a, b, i, n, p; for n from 1 to q do
for i from 1 to ilog10(n) do a:=trunc(n/10^i); b:=n-a*10^i;
if sigma(a*b)=n then print(n); break; fi; od; od; end: P(10^9);
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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*nb)), return (1)); ); } \\ Michel Marcus, Jul 17 2015
(Python)
from sympy import divisor_sigma
for n in range(11, 10**6):
....s = str(n)
....for l in range(1, len(s)):
........m = int(s[:l])*int(s[l:])
........if m > 0 and n == divisor_sigma(m):
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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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