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A119347
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Number of distinct sums of distinct divisors of n.
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5
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1, 3, 3, 7, 3, 12, 3, 15, 7, 15, 3, 28, 3, 15, 15, 31, 3, 39, 3, 42, 15, 15, 3, 60, 7, 15, 15, 56, 3, 72, 3, 63, 15, 15, 15, 91, 3, 15, 15, 90, 3, 96, 3, 63, 55, 15, 3, 124, 7, 63, 15, 63, 3, 120, 15, 120, 15, 15, 3, 168, 3, 15, 59, 127, 15, 144, 3, 63, 15, 142, 3, 195, 3, 15, 63, 63
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If a(n)=sigma(n) (=sum of the divisors of n =A000203(n); i.e. all numbers from 1 to sigma(n) are sums of distinct divisors of n), then n is called a practical number (A005153). The actual sums obtained from the divisors of n are given in row n of the triangle A119348.
The records appear to occur at the highly abundant numbers, A002093, excluding 3 and 10. For n in A174533, a(n) = sigma(n)-2. [From T. D. Noe (noe(AT)sspectra.com), Mar 29 2010]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
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EXAMPLE
| a(5)=3 because the divisors of 5 are 1 and 5 and all the possible sums: are 1,5 and 6; a(6)=12 because we can form all sums 1,2,...,12 by adding up the terms of a nonempty subset of the divisors 1,2,3,6 of 6.
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MAPLE
| with(numtheory): with(linalg): a:=proc(n) local dl, t: dl:=convert(divisors(n), list): t:=tau(n): nops({seq(innerprod(dl, convert(2^t+i, base, 2)[1..t]), i=1..2^t-1)}) end: seq(a(n), n=1..90);
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CROSSREFS
| Cf. A000203, A005153, A119348.
Cf. A093890 [From T. D. Noe (noe(AT)sspectra.com), Mar 29 2010]
Sequence in context: A143275 A083262 A122978 * A062402 A156838 A100587
Adjacent sequences: A119344 A119345 A119346 * A119348 A119349 A119350
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), May 15 2006
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