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A238922
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Numbers n such that Sum_{i=1..j} 1/d(i) - Sum_{i=1..k} 1/p(i) is integer, where p are the prime factors of n, counted with multiplicity, and d its divisors.
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0
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1, 12, 18, 220, 396, 17296, 24016, 287532, 4661056, 64288512, 334144656, 358585488, 555192576, 568719616, 2172649216, 2451538112, 2645953344, 2955423888, 6704333824, 26996772032, 88734733632, 147861504000, 311063879024, 371226582848, 429391876096
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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Divisors of 12 are 1, 2, 3, 4, 6, 12 and 1/1 + 1/2 + 1/3 +1/4 + 1/6 + 1/12 = 7/3. Prime factors of 12 are 2^2, 3 and 1/2 + 1/2 + 1/3 = 4/3. Finally 7/3 - 4/3 = 1 that is integer.
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MAPLE
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with(numtheory); P:=proc(q) local a, b, c, k, n;
for n from 1 to q do if not isprime(n) then b:=sigma(n)/n;
a:=ifactors(n)[2]; c:=add(a[k][2]/a[k][1], k=1..nops(a));
if type(b-c, integer) then lprint(n, b-c); fi; fi; od; end: P(10^6);
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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