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1, 1, 1, 1, 3, 1, 1, 8, 8, 1, 1, 12, 32, 12, 1, 1, 24, 96, 96, 24, 1, 1, 24, 192, 288, 192, 24, 1, 1, 48, 384, 1152, 1152, 384, 48, 1, 1, 48, 768, 2304, 4608, 2304, 768, 48, 1, 1, 72, 1152, 6912, 13824, 13824, 6912, 1152, 72, 1, 1, 72, 1728, 10368, 41472, 41472
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OFFSET
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0,5
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COMMENTS
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We assume that A059381(0)=1 since it would be the empty product.
These are the generalized binomial coefficients associated with the Jordan totient function J_2 given in A007434.
Another name might be the 2-totienomial coefficients.
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LINKS
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FORMULA
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EXAMPLE
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The first five terms in the second Jordan totient function are 1,3,8,12,24 and so T(4,2) = 12*8*3*1/((3*1)*(3*1))=32 and T(5,3) = 24*12*8*3*1/((8*3*1)*(3*1))=96.
The triangle begins
1
1 1
1 3 1
1 8 8 1
1 12 32 12 1
1 24 96 96 24 1
1 24 192 288 192 24 1
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PROG
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(Sage)
q=100 #change q for more rows
P=[0]+[i^2*prod([1-1/p^2 for p in prime_divisors(i)]) for i in [1..q]]
[[prod(P[1:n+1])/(prod(P[1:k+1])*prod(P[1:(n-k)+1])) for k in [0..n]] for n in [0..len(P)-1]] #generates the triangle up to q rows.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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