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 A228884 Determinant of the n X n matrix with (i,j)-entry equal to the greatest common divisor of i-j and n. 2
 1, 3, 20, 128, 2304, 10800, 606528, 3932160, 141087744, 1289945088, 210000000000, 335544320000, 222902511206400, 804545281732608, 39137889484800000, 972777519512027136, 608742554432415203328, 391804906912468697088, 1455817098785971890290688, 968232702940866945220608 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: (i) a(n) is always positive and divisible by Phi(n)^{Phi(n)}*sum_{d|n}Phi(d)*n/d, where Phi(n) is Euler's totient function. (ii) For any composite number n, all prime divisors of a(n) are smaller than n. It is easy to show that a(n) is divisible by sum_[d|n}Phi(d)*n/d) = sum_{k=1,...,n}gcd(k,n), and a(p) = (p-1)^{p-1}*(2p-1) for any prime p. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..100 EXAMPLE a(1) = 1 since gcd(1-1,1) = 1. MATHEMATICA a[n_]:=Det[Table[GCD[i-j, n], {i, 1, n}, {j, 1, n}]] Table[a[n], {n, 1, 20}] CROSSREFS Cf. A228885. Sequence in context: A228750 A187442 A167590 * A138910 A000276 A216778 Adjacent sequences: A228881 A228882 A228883 * A228885 A228886 A228887 KEYWORD nonn AUTHOR Zhi-Wei Sun, Sep 06 2013 STATUS approved

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Last modified September 8 22:39 EDT 2024. Contains 375759 sequences. (Running on oeis4.)