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A070224
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Numbers k such that the sum of p^2, where p are the prime divisors of k, divides the sum of d^2, where d are the divisors of k.
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1
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18, 36, 72, 96, 140, 144, 234, 288, 336, 468, 486, 490, 576, 825, 864, 924, 936, 972, 980, 1008, 1120, 1152, 1248, 1872, 1944, 1960, 2300, 2304, 2310, 2352, 2592, 2673, 2772, 2964, 3024, 3040, 3234, 3332, 3500, 3610, 3744, 3840, 3888, 3920, 4235, 4329
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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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The sum of square divisors of 2352 is sigma_2(2352)=8357910; prime divisors of 2352 are 2,3,7 and (8357910)/(2^2+3^2+7^2)=8357910/62=134805 hence 2352 is in the sequence.
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MAPLE
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filter:= proc(n) (numtheory:-sigma[2](n)/add(p^2, p=numtheory:-factorset(n)))::integer end proc:
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MATHEMATICA
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Select[Range[2, 5000], Divisible[DivisorSigma[2, #], Total[FactorInteger[#][[All, 1]]^2]]&] (* Harvey P. Dale, Apr 02 2018 *)
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PROG
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(PARI) for(n=2, 10000, if(sumdiv(n, d, d^2)%sumdiv(n, d, isprime(d)*d^2)==0, print1(n, ", ")))
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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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STATUS
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approved
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