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A048105
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Number of non-unitary divisors of n.
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27
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0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0, 0, 3, 0, 2, 0, 2, 0, 0, 0, 4, 1, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 5, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 6, 1, 2, 0, 2, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 2, 5, 0, 0, 0, 2, 0, 0, 0, 8, 0, 0, 2, 2, 0, 0, 0, 6, 3, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 2, 0, 0, 0, 8, 0, 2, 2, 5, 0, 0, 0, 4, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
| a[ n ]=Sigma(0, n)-2^r(n), where r()=A001221, the number of distinct primes dividing n.
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EXAMPLE
| Example 1: If n is squarefree (A005117) then a[ n ]=0 since all divisors are unitary. Example 2: n=12, d[ n ]=6, ud[ n ]=4, nud[ 12 ]=d[ 12 ]-ud[ 12 ]=2; from {1,2,3,4,6,12} {1,3,4,12} are unitary while {2,6} are not unitary divisors.
Example 3: n=p^k, a true prime power, d[ n ]=k+1, u[ d ]=2^r[ x ]=2, so nud[ n ]=d[ p^k ]-2=k+1 i,e, it can be arbitrary large.
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PROG
| (Haskell)
a048105 n = length [d | d <- [1..n], mod n d == 0, gcd d (n `div` d) > 1]
-- Reinhard Zumkeller, Aug 17 2011
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CROSSREFS
| a[ n ]=A000005[ n ]-A034444[ n ].
Cf. A056170.
Sequence in context: A110855 A054673 A155103 * A176202 A040081 A113063
Adjacent sequences: A048102 A048103 A048104 * A048106 A048107 A048108
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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