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A051839
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Number of partitions of n with parts (with repetitions) forming a division lattice (i.e. closed under GCD and LCM).
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3
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1, 2, 3, 5, 6, 10, 11, 16, 19, 26, 27, 41, 42, 55, 64, 81, 83, 113, 115, 149, 165, 197, 203, 266, 276, 329, 358, 429, 440, 553, 565, 672, 722, 832, 874, 1060, 1085, 1252, 1342, 1558, 1603, 1901, 1955, 2249, 2410
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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EXAMPLE
| For n=6, the only one of the 11 partitions of 6 that fails is [3,2,1]; so a(6) = 10.
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MAPLE
| with(combinat): ans := []: b := []: for n to 30 do p := partition(n): np := nops(p): nn := np: print(n); for i to np do ss := convert(p[i], set):s := convert(ss, list): ns := nops(s): t := true:
for j to ns-1 do for k from j+1 to ns do if evalb(not(member(gcd(s[j], s[k]), s)) or not(member(lcm(s[j], s[k]), s))) then t := false: fi: od: od:
if t=false then nn := nn-1:fi od: ans := [op(ans), [n, np, nn]]: b := [op(b), [nn]]: od: print(ans); print(b); save b, ans, bans;
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CROSSREFS
| Sequence in context: A072720 A018396 A003238 * A130714 A130689 A024560
Adjacent sequences: A051836 A051837 A051838 * A051840 A051841 A051842
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KEYWORD
| nonn,easy,nice
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AUTHOR
| John McKay (mckay(AT)cs.concordia.ca), Dec 13 1999
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EXTENSIONS
| More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 05 2003
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