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A330683 a(n) is the position of A283980(A025487(n)) in A025487. 8

%I

%S 1,4,11,9,23,20,44,41,22,79,38,73,43,131,69,124,77,212,118,72,201,54,

%T 110,129,327,191,123,312,93,181,209,493,300,199,474,154,286,128,324,

%U 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

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

%H Antti Karttunen, <a href="/A330683/b330683.txt">Table of n, a(n) for n = 1..12868</a>

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

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

%t (* First, load the function f at A025487, then: *)

%t 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 *)

%o (PARI)

%o upto_e = 101;

%o 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

%o 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))); };

%o v330683 = A330683list(upto_e);

%o A330683(n) = v330683[n];

%Y Permutation of A329897.

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

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 26 2019

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Last modified April 13 12:29 EDT 2021. Contains 342936 sequences. (Running on oeis4.)