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A229321
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Composite squarefree numbers n such that p-tau(n) divides n+phi(n), where p are the prime factors of n, tau(n) = A000005(n) and phi(n) = A000010(n).
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7
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6, 10, 15, 21, 39, 110, 170, 609, 897, 935, 1265, 1729, 2882, 2915, 12374, 15387, 161833, 411230, 444797, 558830, 842741, 881705, 1091810, 1122501, 1163990, 1342165, 1565565, 1898259, 2763901, 4157605, 4453697, 4675877, 5962835, 6241610, 6809690, 7201599
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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 1265 are 5, 11, 23 and tau(1265) = 8, phi(1265) = 880. 1265 + 880 = 2145 and 2145 / (5 - 8) = -715, 2145 / (11 - 8) = 715, 2145 / (23 - 8) = 143.
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MAPLE
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with (numtheory); P:=proc(q) global 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 or a[i][1]=tau(n) then ok:=0; break;
else if not type((n+phi(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(6*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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