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A292258 a(1) = 1; for n > 1, a(n) = prime(A101296(n)-1) * a(floor(n/2)).

%I A292258 #12 Sep 23 2017 19:54:31
%S A292258 1,2,2,6,4,10,4,42,18,20,8,110,20,20,20,546,84,198,36,220,100,40,16,
%T A292258 1870,330,100,140,220,40,380,40,12558,2730,420,420,5742,396,180,180,
%U A292258 3740,440,1900,200,440,440,80,32,57970,5610,3630,1650,1100,200,2380,700,3740,1100,200,80,14060,760,200,440,514878
%N A292258 a(1) = 1; for n > 1, a(n) = prime(A101296(n)-1) * a(floor(n/2)).
%H A292258 Antti Karttunen, <a href="/A292258/b292258.txt">Table of n, a(n) for n = 1..8191</a>
%F A292258 a(1) = 1; for n > 1, a(n) = A000040(A101296(n)-1) * a(A004526(n)).
%F A292258 Other identities. For all n >= 1:
%F A292258 A001222(a(n)) = A000523(n).
%F A292258 A007814(a(n)) = A078349(n).
%t A292258 With[{nn = 64}, Block[{s = Function[s, Table[Position[Keys@ s, k_ /; MemberQ[k, n]][[1, 1]], {n, nn}]]@ Map[#1 -> #2 & @@ # &, Transpose@ {Values@ #, Keys@ #}] &@ PositionIndex@ Table[Times @@ MapIndexed[Prime[First@ #2]^#1 &, Sort[FactorInteger[n][[All, -1]], Greater]] - Boole[n == 1], {n, nn}], a}, a[n_] := a[n] = If[n == 1, 1, Prime[s[[n]] - 1]*a[Floor[n/2]]]; Array[a, nn]]] (* _Michael De Vlieger_, Sep 22 2017 *)
%o A292258 (PARI)
%o A292258 up_to = 8191
%o A292258 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A292258 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from _Charles R Greathouse IV_, Aug 17 2011
%o A292258 v101296 = rgs_transform(vector(up_to, n, A046523(n)));
%o A292258 A101296(n) = v101296[n];
%o A292258 A292258(n) = if(1==n,n,prime(A101296(n)-1) * A292258(n\2));
%Y A292258 Cf. A000040, A000523, A004526, A007814, A078349, A101296, A292259 (rgs-version of this filter).
%K A292258 nonn
%O A292258 1,2
%A A292258 _Antti Karttunen_, Sep 22 2017