A300834 - OEIS

%I #6 Mar 19 2018 22:15:11

%S 1,2,2,6,2,30,2,60,10,42,2,4200,2,126,70,660,2,9240,2,13860,210,330,2,

%T 5082000,14,78,220,32760,2,3783780,2,42900,550,780,294,924924000,2,

%U 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

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

%H Antti Karttunen, <a href="/A300834/b300834.txt">Table of n, a(n) for n = 1..3194</a>

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

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

%o (PARI)

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

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

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

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

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

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

%K nonn

%O 1,2

%A _Antti Karttunen_, Mar 18 2018