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A229275
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Composite squarefree numbers n such that p+tau(n) divides n+sigma(n), where p are the prime factors of n, tau(n) = A000005(n) and sigma(n) = A000203(n).
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3
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10778, 16471, 17353, 439453, 1304443, 3719678, 9234253, 17270678, 20512335, 21179143, 50706307, 77292313, 95506557, 103081993, 104707029, 140419077, 240626953, 287947933, 822767689, 982374757, 1608154233, 1918313911, 2219891947, 2471777007, 2632397677
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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 10778 are 2, 17, 317 and sigma(10778) = 17172, tau(10778) = 8.
10778 + 17172 = 27950 and 27950 / (2 + 8) = 2795, 27950 / (17 + 8) = 1118, 27950 / (317 + 8) = 86.
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MAPLE
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with (numtheory); P:=proc(q) local a, b, c, i, ok, p, n;
for n from 2 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+sigma(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(2*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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