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A102467
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Positive integers k such that d(k) <> Omega(k) + omega(k), where d = A000005, Omega = A001222 and omega = A001221.
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9
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1, 12, 18, 20, 24, 28, 30, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 124, 126, 130, 132, 135, 136, 138, 140, 144, 147, 148, 150, 152, 153, 154, 156
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OFFSET
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1,2
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COMMENTS
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These are the numbers which are neither prime powers (>1) nor semiprimes. - M. F. Hasler, Jan 31 2008
For n > 1, positive integers k with a composite divisor, d < k, that is relatively prime to k/d. For example 12 is in the sequence since 4 (composite) is coprime to 12/4 = 3. - Wesley Ivan Hurt, Apr 25 2020
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LINKS
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FORMULA
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EXAMPLE
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10 is not in the sequence since d(10) = 4 is equal to Omega(10) + omega(10) = 2 + 2 = 4.
12 is in the sequence since d(12) = 6 is not equal to Omega(12) + omega(12) = 3 + 2 = 5. - Wesley Ivan Hurt, Apr 25 2020
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MAPLE
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with(numtheory):
q:= n-> is(tau(n)<>bigomega(n)+nops(factorset(n))):
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MATHEMATICA
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Select[Range[200], DivisorSigma[0, #] != PrimeOmega[#] + PrimeNu[#]&] (* Jean-François Alcover, Jun 22 2018 *)
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PROG
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(Sage)
return [k for k in (1..n) if is_A102467(k)]
(Haskell)
a102467 n = a102467_list !! (n-1)
a102467_list = [x | x <- [1..], a000005 x /= a001221 x + a001222 x]
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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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