A300830 - OEIS

A300830

a(n) = Product_{d|n} A019565(d)^(1-A008966(n/d)).

1, 1, 1, 2, 1, 1, 1, 6, 2, 1, 1, 12, 1, 1, 1, 30, 1, 6, 1, 20, 1, 1, 1, 540, 2, 1, 12, 60, 1, 1, 1, 210, 1, 1, 1, 2520, 1, 1, 1, 1260, 1, 1, 1, 84, 20, 1, 1, 94500, 2, 6, 1, 140, 1, 540, 1, 18900, 1, 1, 1, 25200, 1, 1, 60, 2310, 1, 1, 1, 44, 1, 1, 1, 8731800, 1, 1, 12, 132, 1, 1, 1, 346500, 168, 1, 1, 39600, 1, 1, 1, 41580, 1, 1260

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OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8192

FORMULA

a(n) = Product_{d|n} A019565(d)^(1-abs(A008683(n/d))).

a(n) = A293214(n) / (A300831(n)*A300832(n)).

PROG

(PARI)

A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565

A300830(n) = { my(m=1); fordiv(n, d, if(!moebius(n/d), m *= A019565(d))); m; };