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A066663 Numbers n such that phi(n) is a proper substring of n. 3
1320, 1640, 1768, 1996, 2640, 3960, 13200, 16400, 19984, 19996, 26400, 39600, 132000, 164000, 199996, 264000, 396000, 1320000, 1640000, 1999936, 2640000, 3960000, 13200000, 16400000, 16666240, 17999488, 18515584, 19999984, 19999996 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Since the ratio n/phi(n) grows very slowly with n (see A091439), this sequence will be equal to A067206 (apart the initial 1) at least for all the terms smaller than 10^103. - Giovanni Resta, Apr 14 2017

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..65 (terms < 10^12)

EXAMPLE

phi(1320)=320, phi(1640)=640, phi(1768)=768, phi(1996)=996, phi(2640)=640,..., phi(199999999984)=99999999984.

MAPLE

with(numtheory); P:=proc(q) local a, b, n;

for n from 2 to q do a:=phi(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od;

if phi(n)=(n mod 10^b) then print(n); fi; od; end: P(10^9); # Paolo P. Lava, Mar 13 2014

MATHEMATICA

Select[Range[2, 10^5], StringPosition[ ToString@ #, ToString@ EulerPhi@ #] != {} &] (* Giovanni Resta, Apr 14 2017 *)

CROSSREFS

Cf. A000010, A036433, A091439, A067206.

Sequence in context: A200202 A255799 A023318 * A067206 A248857 A260839

Adjacent sequences:  A066660 A066661 A066662 * A066664 A066665 A066666

KEYWORD

nonn,base

AUTHOR

Vladeta Jovovic, Jan 11 2002

EXTENSIONS

Offset corrected and a(19)-a(29) from Donovan Johnson, May 08 2010

STATUS

approved

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Last modified September 24 19:49 EDT 2022. Contains 356949 sequences. (Running on oeis4.)