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A228299
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Composite squarefree numbers n such that p+d(n) divides n+d(n), where p are the prime factors of n and d(n) the number of divisors of n.
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16
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21098, 134930, 343027, 361730, 387127, 751394, 793595, 1344517, 1430449, 1579394, 1794854, 3542797, 5022254, 7930117, 9241627, 12122947, 21089129, 21928717, 49825117, 70233329, 78795074, 90079589, 95208734, 110995807, 124648303, 124964219, 144871634
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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Prime factors of 21098 are 2, 7, 11 and 137 while d(21098) = 16. We have that 21098 + 16 = 21114 and 21114 / (2 + 16) = 1173, 21114 / (7 + 16) = 918, 21114 / (11 + 16) = 782 and 21114 / (137 + 16) = 138.
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MAPLE
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with (numtheory); P:=proc(q) local a, i, ok, n;
for n from 1 to q do if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
for i from 1 to nops(a) do if a[i][2]>1 then ok:=0; break;
else if not type((n+tau(n))/(a[i][1]+tau(n)), integer) then ok:=0; break; fi; fi; od; if ok=1 then print(n); fi; fi; od; end: P(10^6);
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CROSSREFS
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KEYWORD
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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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