

A063507


Least k such that k  phi(k) = n, or 0 if no such k exists.


6



2, 4, 9, 6, 25, 10, 15, 12, 21, 0, 35, 18, 33, 26, 39, 24, 65, 34, 51, 38, 45, 30, 95, 36, 69, 0, 63, 52, 161, 42, 87, 48, 93, 0, 75, 54, 217, 74, 99, 76, 185, 82, 123, 60, 117, 66, 215, 72, 141, 0, 235, 0, 329, 78, 159, 98, 105, 0, 371, 84, 177, 122, 135, 96, 305, 90, 427
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Inverse cototient (A051953) sets represented by their minimum, as in A002181 for totient function. Impossible values (A005278) are replaced by zero.
If a(n) > 0, then it appears that a(n) > 1.26n.  T. D. Noe, Dec 06 2006


LINKS

T. D. Noe, Table of n, a(n) for n=1..10000


FORMULA

a(n)A051953(a(n)) = n if possible and a(n)=0 if n belongs to A005278.


EXAMPLE

x = InvCototient[24] = {36, 40, 44, 46}; Phi[x] = Phi[{36, 40, 44, 46}] = {12, 16, 20, 22}; xPhi[x] = {24, 24, 24, 24}, so a(24) = Min[InvCototient[24]]; a(10) = 0 because 10 is in A005278.


MATHEMATICA

Table[SelectFirst[Range[n^2 + 1], #  EulerPhi[#] == n &] /. k_ /; ! IntegerQ@ k > 0, {n, 67}] (* Michael De Vlieger, Jan 11 2018 *)


CROSSREFS

Cf. A051953, A000010, A002181, A005277, A005278.
Cf. A063748 (greatest solution to xphi(x)=n).
Cf. A063740 (number of k such that cototient(k) = n).
Sequence in context: A104654 A011182 A304753 * A241473 A055858 A141389
Adjacent sequences: A063504 A063505 A063506 * A063508 A063509 A063510


KEYWORD

nonn


AUTHOR

Labos Elemer, Aug 09 2001


EXTENSIONS

Edited by N. J. A. Sloane, Oct 25 2008 at the suggestion of R. J. Mathar


STATUS

approved



