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A048146
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Sum of non-unitary divisors of n.
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21
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0, 0, 0, 2, 0, 0, 0, 6, 3, 0, 0, 8, 0, 0, 0, 14, 0, 9, 0, 12, 0, 0, 0, 24, 5, 0, 12, 16, 0, 0, 0, 30, 0, 0, 0, 41, 0, 0, 0, 36, 0, 0, 0, 24, 18, 0, 0, 56, 7, 15, 0, 28, 0, 36, 0, 48, 0, 0, 0, 48, 0, 0, 24, 62, 0, 0, 0, 36, 0, 0, 0, 105, 0, 0, 20, 40, 0, 0, 0, 84, 39, 0, 0, 64, 0, 0, 0, 72, 0, 54, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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FORMULA
| a(n) = A000203[n] - A034448[n] = sigma(n) - usigma(n). a(1) = 0, a(p) = 0, a(pq) = 0, a(pq...z) = 0, a(p^k) = (p^k - p) / (p - 1), for p = primes (A000040), pq = product of two distinct primes (A006881), pq...z = product of k (k >=2) distinct primes p, q, ..., z (A120944), p^k = prime powers (A000961(n) for n > 1) k = natural numbers (A000027).
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EXAMPLE
| If n = 1000, the 12 non-unitary divisors are {2, 4, 5, 10, 20, 25, 40, 50, 100, 200, 250, 500} and their sum is a[ n ] = a[ 1000 ] = 1206. a(16) = a(2^4) = (2^4 - 2) / (2 - 1)= 14.
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MATHEMATICA
| us[n_Integer] := (d = Divisors[n]; l = Length[d]; k = 1; s = n; While[k < l, If[ GCD[ d[[k]], n/d[[k]] ] == 1, s = s + d[[k]]]; k++ ]; s); Table[ DivisorSigma[1, n] - us[n], {n, 1, 100} ]
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CROSSREFS
| Cf. A034444, A000203, A048105-A048107, A048109, A048111, A005117.
Sequence in context: A053203 A158360 A094315 * A028973 A066503 A057385
Adjacent sequences: A048143 A048144 A048145 * A048147 A048148 A048149
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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EXTENSIONS
| Edited by Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 01 2009
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