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A161917
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Numbers n for which the sum of their prime factors (with repetition) divides the sum of their divisors.
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5
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12, 15, 35, 42, 60, 63, 66, 68, 84, 90, 95, 110, 114, 119, 140, 143, 152, 168, 189, 195, 204, 209, 216, 234, 245, 258, 264, 270, 280, 287, 290, 294, 297, 319, 322, 323, 352, 368, 377, 380, 384, 396, 470, 476, 480, 506, 510, 527, 531, 544, 552, 558, 559, 572
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history;
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internal format)
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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n=12: Sum_divisors (1,2,3,4,6,12) = 28; Sum_prime_factors (2,2,3) =7 -> 28/7 = 4. n=319: Sum_divisors (1,11,29,319) = 360; Sum_prime_factors (11,29) =40 -> 360/40 = 9.
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MAPLE
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with(numtheory); P:=proc(q) local a, n;
for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2];
if type(sigma(n)/add(a[k][1]*a[k][2], k=1..nops(a)), integer) then print(n);
fi; fi; od; end: P(10^4);
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MATHEMATICA
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Select[Range[2, 600], Divisible[DivisorSigma[1, #], Total[ Times@@@ FactorInteger[#]]]&] (* Harvey P. Dale, Dec 09 2010 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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