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A330683 a(n) is the position of A283980(A025487(n)) in A025487. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 11 21:35 EDT 2021. Contains 343808 sequences. (Running on oeis4.)