A330683 a(n) is the position of A283980(A025487(n)) in A025487.

1, 4, 11, 9, 23, 20, 44, 41, 22, 79, 38, 73, 43, 131, 69, 124, 77, 212, 118, 72, 201, 54, 110, 129, 327, 191, 123, 312, 93, 181, 209, 493, 300, 199, 474, 154, 286, 128, 324, 725, 190, 454, 147, 272, 310, 697, 245, 434, 208, 490, 1044, 299, 671, 114, 232, 416, 469, 1008, 374, 646, 321, 721, 1481, 451, 974, 186, 359

Offset: 1

Author

Antti Karttunen, Dec 26 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12868

Crossrefs

Permutation of A329897.

Cf. A025487, A085089, A101296, A181815, A283980, A329898 (positive integers not in this sequence), A329904 (a left inverse), A329906, A330681.

Programs

Mathematica

(* First, load the function f at A025487, then: *)
With[{s = Union@ Flatten@ f@ 10}, TakeWhile[#, # != 0 &] &@ Map[If[# > Max@ s, 0, FirstPosition[s, #][[1]] ] &[(Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}] - Boole[# == 1])*2^IntegerExponent[#, 2]] &, s]] (* Michael De Vlieger, Jan 11 2020 *)

PARI

upto_e = 101;
A283980(n) = {my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==2, 6, nextprime(p+1))^e)}; \\ From A283980
A330683list(e) = { my(lista = List([1, 2]), i=2, u = 2^e, t, v025487); while(lista[i] != u, if(2*lista[i] <= u, listput(lista,2*lista[i]); t = A283980(lista[i]); if(t <= u, listput(lista,t))); i++); v025487 = vecsort(Vec(lista)); lista = List([]); for(i=1,oo,if(!(t=vecsearch(v025487,A283980(v025487[i]))),return(Vec(lista)), listput(lista,t))); };
v330683 = A330683list(upto_e);
A330683(n) = v330683[n];

Formula

a(n) = A085089(A330681(n)) = A101296(A330681(n)) = A101296(A283980(A025487(n))).

For all n >= 1, A329904(a(n)) = n.