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A238967
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Maximal size of an antichain in canonical order.
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2
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1, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 6, 1, 2, 3, 4, 5, 7, 10, 1, 2, 3, 4, 4, 6, 8, 7, 10, 14, 20, 1, 2, 3, 4, 4, 6, 8, 7, 8, 11, 15, 13, 18, 25, 35, 1, 2, 3, 4, 4, 6, 8, 5, 8, 9, 12, 16, 10, 14, 16, 22, 30, 19, 26, 36, 50, 70, 1, 2, 3, 4, 4, 6, 8, 5, 8, 9, 12, 16, 9, 11, 15, 17, 23, 31, 12, 19, 26, 22, 30, 41, 56, 35, 48, 66, 91, 126
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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Triangle T(n,k) begins:
1;
1;
1, 2;
1, 2, 3;
1, 2, 3, 4, 6;
1, 2, 3, 4, 5, 7, 10;
1, 2, 3, 4, 4, 6, 8, 7, 10, 14, 20;
...
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MAPLE
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with(numtheory):
f:= n-> (m-> add(`if`(bigomega(d)=m, 1, 0),
d=divisors(n)))(iquo(bigomega(n), 2)):
b:= (n, i)-> `if`(n=0 or i=1, [[1$n]], [map(x->
[i, x[]], b(n-i, min(n-i, i)))[], b(n, i-1)[]]):
T:= n-> map(x-> f(mul(ithprime(i)^x[i], i=1..nops(x))), b(n$2))[]:
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PROG
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b(n)={my(h=bigomega(n)\2); sumdiv(n, d, bigomega(d)==h)}
N(sig)={prod(k=1, #sig, prime(k)^sig[k])}
Row(n)={apply(s->b(N(s)), vecsort([Vecrev(p) | p<-partitions(n)], , 4))}
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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Offset changed and terms a(50) and beyond from Andrew Howroyd, Mar 25 2020
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STATUS
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approved
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