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A200070
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Numbers n such that the sum of the prime divisors equals 2 times the difference between the largest and the smallest prime divisor.
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4
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110, 182, 220, 364, 374, 440, 494, 550, 728, 748, 782, 880, 988, 1100, 1210, 1274, 1334, 1456, 1496, 1564, 1760, 1976, 2200, 2294, 2366, 2420, 2548, 2668, 2750, 2912, 2992, 3128, 3182, 3520, 3854, 3952, 4114, 4400, 4588, 4732, 4840, 4982, 5096, 5336, 5500
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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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98420 is in the sequence because the prime divisors are 2, 5, 7, 19, 37 and the sum 2 + 5 + 7 + 19 + 37 = 70 = 2*(37 - 2).
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MAPLE
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filter:= proc(n) local P; P:= numtheory:-factorset(n);
convert(P, `+`) = 2*(max(P)-min(P))
end proc:
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MATHEMATICA
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Select[Range[5500], Plus@@((pl=First/@FactorInteger[#])/2)==pl[[-1]]-pl[[1]]&]
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PROG
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(PARI) isok(n) = if (n>1, my(f=factor(n)[, 1]); 2*(vecmax(f) - vecmin(f)) == vecsum(f)); \\ Michel Marcus, Apr 10 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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