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A224346
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Numbers n such that Sum_{i=1..k} 1/p(i) + Sum_{i=1..j} 1/d(i) is integer, where p are the prime factors of n, counted with multiplicity, and d its divisors.
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3
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1, 2, 21, 44, 560, 752, 2064, 12224, 98595, 38735300, 53668332, 147728896, 407729196, 423212608, 516441712, 1227777925, 1323319996, 20440128681, 153088685248, 206158168064, 375868306368, 798666196041
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OFFSET
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1,2
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COMMENTS
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If (Sum_{i=1..k} 1/p(i)) * (Sum_{i=1..j} 1/d(i)) is considered, for n between 1 and 10^6, only 1080 gives an integer value: 27/10 * 10/3 = 9.
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LINKS
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EXAMPLE
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n=44; its prime factors are 2^2, 11 while its divisors are 1, 2, 4, 11, 22, 44 and 1/2 + 1/2 + 1/11 + 1/1 + 1/2 + 1/4 + 1/11 + 1/22 + 1/44 = 3.
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MAPLE
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with(numtheory); List224346:=proc(q) local a, b, c, j, n;
for n from 1 to q do
a:=ifactors(n)[2]; b:=0; for j from 1 to nops(a) do b:=b+a[j, 2]/a[j, 1]; od;
c:=sigma(n)/n; if type(b+c, integer) then print(n); fi; od; end:
List224346(10^6);
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MATHEMATICA
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Select[Range[10^5], Mod[DivisorSigma[1, #] + Total[# / Divide @@@ FactorInteger@#], #] == 0 &] (* Giovanni Resta, Apr 10 2013 *)
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CROSSREFS
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KEYWORD
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nonn,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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