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A228302
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Composite squarefree numbers n such that p+d(n) divides n-d(n) for all prime factors p of n, where d(n) is the number of divisors of n.
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16
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4958, 51653, 55583, 1251574, 4909102, 5430797, 5785073, 6096931, 13892243, 14058781, 14809517, 16699426, 27391073, 32426566, 32673383, 38669686, 43459682, 44762461, 53638783, 69836866, 74975761, 75226313, 85607461, 96973703, 105139141, 122864065
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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 51653 are 7, 47 and 157 while d(51653) = 8. We have that 51653 - 8 = 51645 and 51645 / (7 + 8) = 3443, 51645 / (47 + 8) = 939 and 51645 / (157 + 8) = 313.
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MAPLE
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with(numtheory); P:=proc(q) local a, i, ok, p, n;
for n from 1 to q do if not isprime(n) and issqrfree(n) then
a:=ifactors(n)[2]; ok:=1; for i from 1 to nops(a) do
if not type((n-tau(n))/(a[i][1]+tau(n)), integer) then ok:=0; break; fi; od;
if ok=1 then print(n); fi; fi; od; end: P(10^9);
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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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