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Search: id:A164988
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| A164988 |
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Number of ways to select disjoint subsets out of {1..n} such that their (sorted) element sums give the list of divisors of n. |
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+0
1
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| 1, 1, 1, 1, 2, 1, 3, 2, 3, 3, 7, 2, 10, 9, 7, 9, 21, 8, 29, 12, 31, 67, 56, 11, 79, 167, 105, 85, 137, 37, 181, 248, 346, 893, 299, 106, 404, 1974, 993, 338, 669, 724, 853, 3335, 1068, 8757, 1371, 852, 2422, 9157, 7124, 17168, 2702, 11606, 6390, 10782, 17681, 68538
(list; graph; listen)
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OFFSET
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1,5
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EXAMPLE
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a(9) = 3: subset selections are [{1},{3},{9}], [{1},{3},{2,7}], [{1},{3},{4,5}].
a(10) = 3: [{1},{2},{5},{10}], [{1},{2},{5},{3,7}], [{1},{2},{5},{4,6}].
a(11) = 7: [{1},{11}], [{1},{2,9}], [{1},{3,8}], [{1},{4,7}], [{1},{5,6}], [{1},{2,3,6}], [{1},{2,4,5}].
a(12) = 2: [{1},{2},{3},{4},{6},{12}], [{1},{2},{3},{4},{6},{5,7}].
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MAPLE
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with (numtheory): b:= proc() option remember; local i, j, t, m; m:= args[nargs]; if nargs=1 then 1 elif args[1]=0 then b (args[t] $t=2..nargs) elif m=0 or add (args[i], i=1..nargs-1)> m*(m+1)/2 then 0 else b (args[t] $t=1..nargs-1, m-1) +add (`if` (args[j]-m<0, 0, b (sort ([seq (args[i] -`if` (i=j, m, 0), i=1..nargs-1)])[], m-1)), j=1..nargs-1) fi end: a:= n-> b (divisors(n)[], n): seq (a(n), n=1..40);
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CROSSREFS
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Cf. A065205, A035470.
Sequence in context: A053262 A007359 A158206 this_sequence A115872 A133926 A144337
Adjacent sequences: A164985 A164986 A164987 this_sequence A164989 A164990 A164991
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KEYWORD
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nice,nonn
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 03 2009
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