A194507 a(n) = y is the unique solution to y*phi(y) = A082473(n).

1, 2, 3, 4, 6, 5, 8, 10, 7, 12, 9, 14, 18, 11, 15, 16, 13, 20, 24, 22, 30, 21, 17, 26, 28, 19, 36, 27, 25, 42, 23, 32, 34, 40, 33, 38, 48, 29, 35, 44, 31, 39, 60, 54, 50, 46, 45, 52, 66, 37, 56, 58, 51, 41, 70, 72, 43, 62, 78, 84, 64, 57, 49, 90, 47, 68, 55, 63, 80

Offset: 1

Author

Franz Vrabec, Aug 27 2011

Keywords

• nonn

Comments

The permutation which rearranges the terms of A002618 into ascending order. - Antti Karttunen, Sep 28 2019

Examples

			a(6) = 5 because 5*phi(5) = 20 = A082473(6).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20001
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A002618, A082473, A327173 (inverse permutation).

Nonzero terms in A327172, in the order of appearance.

Programs

Mathematica

Block[{nn = 3000, s, t}, s = Array[EulerPhi[#] (Sqrt@ # /. (c_: 1) a_^(b_: 0) :> (c a^b)^2) &, nn]; t = TakeWhile[Union@ s, # <= nn &]; Map[Block[{y = 1}, While[y EulerPhi@ y != #, y++]; y] &, t]] (* Michael De Vlieger, Sep 29 2019, after Bill Gosper at A007913 *)

PARI

up_to = 105;
A327172(n) = { fordiv(n,d,if(eulerphi(d)*d == n, return(d))); (0); };
A194507list(up_to) = { my(v=vector(up_to),k=1); for(n=1,oo,if((v[k]=A327172(n))>0,k++); if(k>up_to, return(v))); };
v194507 = A194507list(up_to);
A194507(n) = v194507[n]; \\ Antti Karttunen, Sep 28 2019

Formula

From Antti Karttunen, Sep 28 2019: (Start)

a(n) = A327172(A082473(n)).

A002618(a(n)) = A082473(n).

(End)