A300834 - OEIS

A300834

a(n) = Product_{d|n, d<n} A019565(A003714(d)), where A003714(n) is the n-th Fibbinary number.

1, 2, 2, 6, 2, 30, 2, 60, 10, 42, 2, 4200, 2, 126, 70, 660, 2, 9240, 2, 13860, 210, 330, 2, 5082000, 14, 78, 220, 32760, 2, 3783780, 2, 42900, 550, 780, 294, 924924000, 2, 1092, 130, 41621580, 2, 3898440, 2, 112200, 60060, 306, 2, 28078050000, 42, 235620, 1300, 92820, 2, 200119920, 770, 128648520, 1820, 1122, 2, 424964656116000, 2, 3366

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OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..3194

FORMULA

a(n) = Product_{d|n, d<n} A019565(A003714(d)).

For n >= 1, A001222(a(n)) = A300836(n).

PROG

(PARI)

A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649

A003714(n) = { my(s=0, w); while(n>2, w = A072649(n); s += 2^(w-1); n -= fibonacci(w+1)); (s+n); }

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

A300834(n) = { my(m=1); fordiv(n, d, if(d < n, m *= A019565(A003714(d)))); m; };

CROSSREFS

Cf. A003714, A019565, A300835 (rgs-transform of this sequence), A300836.

Cf. also A293214, A293216, A293221, A293222, A293231.

Sequence in context: A306387 A308692 A319352 * A293214 A293216 A319708

Adjacent sequences: A300831 A300832 A300833 * A300835 A300836 A300837

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 18 2018

STATUS

approved