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A324938
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a(n) = the number of values of m such that the sum of proper unitary divisors of m (A034460) is n.
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6
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0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 3, 1, 3, 2, 3, 3, 2, 2, 3, 3, 4, 3, 2, 3, 3, 3, 4, 4, 3, 3, 3, 5, 4, 5, 4, 5, 2, 4, 4, 5, 4, 5, 3, 5, 5, 5, 2, 6, 3, 6, 4, 6, 3, 7, 3, 6, 4, 5, 3, 7, 3, 5, 4, 6, 2, 8, 2, 6, 5, 7, 2, 8, 4, 6, 7, 7, 4, 9, 2, 7, 4, 5, 4, 9, 3, 9
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OFFSET
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2,7
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COMMENTS
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The offset is 2 as in A048138 since there are infinitely many numbers (all the powers of primes) for which A034460 = 1.
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LINKS
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FORMULA
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EXAMPLE
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a(8) = 2 since 8 is the sum of the proper unitary divisors of 10 (1 + 2 + 5) and 12 (1 + 3 + 4).
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MATHEMATICA
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us[1] = 0; us[n_] := Times @@ (1 + Power @@@ FactorInteger[n]) - n; m = 100; v = Table[0, {m}]; Do[u = us[k]; If[2 <= u <= m, v[[u]]++], {k, 1, m^2}]; Rest @ v
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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