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A238963
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Number of divisors of A063008(n,k).
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9
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1, 2, 3, 4, 4, 6, 8, 5, 8, 9, 12, 16, 6, 10, 12, 16, 18, 24, 32, 7, 12, 15, 20, 16, 24, 32, 27, 36, 48, 64, 8, 14, 18, 24, 20, 30, 40, 32, 36, 48, 64, 54, 72, 96, 128, 9, 16, 21, 28, 24, 36, 48, 25, 40, 45, 60, 80, 48, 64, 72, 96, 128, 81, 108, 144, 192, 256, 10, 18, 24, 32, 28, 42, 56, 30, 48, 54, 72, 96, 50, 60, 80, 90, 120, 160, 64, 96, 128, 108, 144, 192, 256, 162, 216, 288, 384, 512
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OFFSET
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0,2
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COMMENTS
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Equivalent to A074139 but using canonical order.
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LINKS
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FORMULA
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Trow(n) = List_{p in Partitions(n)} (Product_{t in p}(t + 1)). # Peter Luschny, Dec 11 2023
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EXAMPLE
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Triangle begins:
1;
2;
3, 4;
4, 6, 8;
5, 8, 9, 12, 16;
6, 10, 12, 16, 18, 24, 32;
7, 12, 15, 20, 16, 24, 32, 27, 36, 48, 64;
...
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MAPLE
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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-> numtheory[tau](mul(ithprime(i)
^x[i], i=1..nops(x))), b(n$2))[]:
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PROG
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b(n)={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))}
(SageMath)
def A238963row(n):
return list(product(t + 1 for t in p) for p in Partitions(n))
print([A238963row(n) for n in range(10)]) # Peter Luschny, Dec 11 2023
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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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STATUS
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approved
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