A246063 First occurrence of n in sequence A112329.

2, 1, 3, 9, 15, 64, 45, 256, 96, 144, 192, 4096, 240, 16384, 768, 576, 480, 262144, 720, 1048576, 960, 2304, 12288, 16777216, 1440, 5184, 49152, 3600, 3840, 1073741824, 2880, 4294967296, 3360, 36864, 786432, 20736, 5040, 274877906944, 3145728, 147456, 6720

Offset: 0

Author

Ray Chandler, Aug 24 2014

Keywords

• nonn

Comments

Inspired by a comment from Robert G. Wilson v in sequence A112329.

Links

• Ray Chandler, Table of n, a(n) for n = 0..3322 [terms <= 1000 digits]

Crossrefs

Cf. A094572, A112329.

Programs

Mathematica

g[lst_,p_]:=Module[{t,i,j},Union[Flatten[Table[t=lst[[i]];t[[j]]=p*t[[j]];Sort[t],{i,Length[lst]},{j,Length[lst[[i]]]}],1],Table[Sort[Append[lst[[i]],p]],{i,Length[lst]}]]];f[n_]:=Module[{i,j,p,e,lst={{}}},{p,e}=Transpose[FactorInteger[n]];Do[lst=g[lst,p[[i]]],{i,Length[p]},{j,e[[i]]}];lst];
(* above factor functions from T. D. Noe in A162247 *)
nmax=100;
a1={2,1,3};
Do[
least=Infinity;
fn=f[n];
Do[
exps=Reverse[fnitem]-1;
odd=even=1;
cnt=0;
Do[
cnt++;
odd*=(Prime[cnt+1]^exp);
even*=(Prime[cnt]^exp);
,{exp,exps}];
least=Min[least,odd,4even];
,{fnitem,fn}];
AppendTo[a1,least];
,{n,3,nmax}];
a1

PARI

d(n) = if (denominator(n)==1, numdiv(n), 0);
f(n) = numdiv(n) - 2*d(n/2) + 2*d(n/4);
a(n) = {my(k = 1); while (f(k) != n, k++); k;} \\ Michel Marcus, Jul 30 2017

Formula

a(p) = 2^(p+1) for prime p >= 5.