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A191580
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Numbers n for which the sum of their prime factors (with repetition) divides the sum of their anti-divisors.
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3
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5, 10, 40, 41, 129, 135, 140, 155, 182, 189, 200, 204, 206, 238, 375, 429, 435, 441, 455, 475, 546, 564, 574, 616, 625, 678, 722, 744, 765, 836, 856, 902, 1035, 1056, 1170, 1188, 1272, 1296, 1344, 1518, 1650, 1764, 1806, 1918, 1925
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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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40-> sum prime factors=2+2+2+5=11; sum anti-divisors=3+9+16+27=55; 55/11=5
129-> sum prime factors=3+43=46; sum anti-divisors=2+6+7+37+86=138; 138/46=3
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MAPLE
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with(numtheory); P:=proc(i) local a, b, j, k, s, n;
for n from 3 to i do b:=ifactors(n)[2];
s:=add(b[k][1]*b[k][2], k=1..nops(b));
k:=0; j:=n; while j mod 2<>1 do k:=k+1; j:=j/2; od; a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
if type(a/s, integer) then print(n); fi; od; end: P(2000);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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