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A246063 First occurrence of n in sequence A112329. 2

%I #18 Jul 31 2017 12:58:50

%S 2,1,3,9,15,64,45,256,96,144,192,4096,240,16384,768,576,480,262144,

%T 720,1048576,960,2304,12288,16777216,1440,5184,49152,3600,3840,

%U 1073741824,2880,4294967296,3360,36864,786432,20736,5040,274877906944,3145728,147456,6720

%N First occurrence of n in sequence A112329.

%C Inspired by a comment from _Robert G. Wilson v_ in sequence A112329.

%H Ray Chandler, <a href="/A246063/b246063.txt">Table of n, a(n) for n = 0..3322</a> [terms <= 1000 digits]

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

%t 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];

%t (* above factor functions from _T. D. Noe_ in A162247 *)

%t nmax=100;

%t a1={2,1,3};

%t Do[

%t least=Infinity;

%t fn=f[n];

%t Do[

%t exps=Reverse[fnitem]-1;

%t odd=even=1;

%t cnt=0;

%t Do[

%t cnt++;

%t odd*=(Prime[cnt+1]^exp);

%t even*=(Prime[cnt]^exp);

%t ,{exp,exps}];

%t least=Min[least,odd,4even];

%t ,{fnitem,fn}];

%t AppendTo[a1,least];

%t ,{n,3,nmax}];

%t a1

%o (PARI) d(n) = if (denominator(n)==1, numdiv(n), 0);

%o f(n) = numdiv(n) - 2*d(n/2) + 2*d(n/4);

%o a(n) = {my(k = 1); while (f(k) != n, k++); k;} \\ _Michel Marcus_, Jul 30 2017

%Y Cf. A094572, A112329.

%K nonn

%O 0,1

%A _Ray Chandler_, Aug 24 2014

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)