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Search: id:A100577
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| A100577 |
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Number of sets of divisors of n with an odd sum. |
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+0
1
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| 1, 2, 2, 4, 2, 8, 2, 8, 4, 8, 2, 32, 2, 8, 8, 16, 2, 32, 2, 32, 8, 8, 2, 128, 4, 8, 8, 32, 2, 128, 2, 32, 8, 8, 8, 256, 2, 8, 8, 128, 2, 128, 2, 32, 32, 8, 2, 512, 4, 32, 8, 32, 2, 128, 8, 128, 8, 8, 2, 2048, 2, 8, 32, 64, 8, 128, 2, 32, 8, 128, 2, 2048, 2, 8, 32, 32, 8, 128, 2, 512, 16, 8, 2
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = A000079(A032741(n)).
Also number of subsets of divisors of n which do not contain 1; thus a(n) = (A100587(n)+1)/2. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 02 2007
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FORMULA
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a(n) = 2^(A000005(n)-1).
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EXAMPLE
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a(12) = #{{1}, {3}, {1,2}, {1,4}, {2,3}, {1,6}, {3,4},
{1,2,4}, {3,6}, {1,2,6}, {2,3,4}, {1,4,6}, {2,3,6}, {1,12}, {3,4,6},
{1,2,4,6}, {3,12}, {1,2,12}, {2,3,4,6}, {1,4,12}, {2,3,12}, {1,6,12},
{3,4,12}, {1,2,4,12}, {3,6,12}, {1,2,6,12}, {2,3,4,12}, {1,4,6,12},
{2,3,6,12}, {1,2,4,6,12}, {3,4,6,12}, {2,3,4,6,12}} = 32.
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CROSSREFS
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Cf. A001227.
Sequence in context: A003980 A132801 A072478 this_sequence A018818 A067538 A096154
Adjacent sequences: A100574 A100575 A100576 this_sequence A100578 A100579 A100580
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Nov 29 2004
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