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A238974
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The size (the number of arcs) in the transitive closure of divisor lattice in canonical order.
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2
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0, 1, 3, 5, 6, 12, 19, 10, 22, 27, 42, 65, 15, 35, 48, 74, 90, 138, 211, 21, 51, 75, 115, 84, 156, 238, 189, 288, 438, 665, 28, 70, 108, 165, 130, 240, 365, 268, 324, 492, 746, 594, 900, 1362, 2059, 36, 92, 147, 224, 186, 342, 519, 200, 410, 495, 750, 1135, 552, 836, 1008, 1524, 2302, 1215, 1836, 2772, 4182, 6305
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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Triangle T(n,k) begins:
0;
1;
3, 5;
6, 12, 19;
10, 22, 27, 42, 65;
15, 35, 48, 74, 90, 138, 211;
21, 51, 75, 115, 84, 156, 238, 189, 288, 438, 665;
...
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MAPLE
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with(numtheory):
f:= n-> add(tau(d), d=divisors(n) minus {n}):
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) = {sumdivmult(n, d, numdiv(d)) - numdiv(n)}
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 26 2020
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STATUS
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approved
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