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A199857
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Numbers such that the sum of the squares of the largest and the smallest prime divisor equals the sum of the squares of the other distinct prime divisors.
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1
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24871, 81719, 81809, 88711, 174097, 198679, 201761, 256151, 273581, 290191, 329681, 405449, 422807, 428281, 472549, 572663, 592999, 604279, 620977, 701561, 728119, 752191, 770431, 876641, 898909, 1011839, 1063517, 1121729, 1178879, 1218679, 1251439, 1389223
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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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24871 is in the sequence because the prime distinct divisors are {7, 11, 17, 19} and 19^2 + 7^2 = 11^2 + 17^2 = 410.
Although the early terms are all odd with four distinct prime factors, 7212590 = 2 * 5 * 7 * 11 * 17 * 19 * 29 has seven distinct prime factors, and 2^2 + 29^2 = 5^2 + 7^2 + 11^2 + 17^2 + 19^2 = 845. - D. S. McNeil, Nov 12 2011
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MAPLE
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isA199857 := proc(n)
local p;
p := sort(convert((numtheory[factorset](n)), list)) ;
if nops(p) >= 3 then
return ( op(1, p)^2 + op(-1, p)^2 = add(op(i, p)^2, i=2..nops(p)-1) ) ;
else
false;
end if;
end proc:
for n from 2 to 1500000 do
if isA199857(n) then
printf("%d, ", n) ;
end if ;
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MATHEMATICA
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Select[Range[1400000], Plus@@((pl=First/@FactorInteger[#])^2/2) == pl[[1]]^2+pl[[-1]]^2&] (* program from Ray Chandler adapted for this sequence - see A199745 *)
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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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