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

1, 2, 2, 6, 4, 10, 4, 42, 18, 20, 8, 110, 20, 20, 20, 546, 84, 198, 36, 220, 100, 40, 16, 1870, 330, 100, 140, 220, 40, 380, 40, 12558, 2730, 420, 420, 5742, 396, 180, 180, 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

Offset: 1

Author

Antti Karttunen, Sep 22 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191

Crossrefs

Cf. A000040, A000523, A004526, A007814, A078349, A101296, A292259 (rgs-version of this filter).

Programs

Mathematica

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 *)

PARI

up_to = 8191
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; };
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
v101296 = rgs_transform(vector(up_to, n, A046523(n)));
A101296(n) = v101296[n];
A292258(n) = if(1==n,n,prime(A101296(n)-1) * A292258(n\2));

Formula

a(1) = 1; for n > 1, a(n) = A000040(A101296(n)-1) * a(A004526(n)).

Other identities. For all n >= 1:

A001222(a(n)) = A000523(n).

A007814(a(n)) = A078349(n).