A330683 - OEIS

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

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OFFSET

1,2

LINKS

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

FORMULA

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

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

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 *)

PROG

(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];

CROSSREFS

Permutation of A329897.

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

Sequence in context: A096735 A211458 A222284 * A020949 A210693 A168212

Adjacent sequences: A330680 A330681 A330682 * A330684 A330685 A330686

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 26 2019

STATUS

approved