A082060 -id:A082060 - cp's OEIS frontend

A115921 Numbers k such that the decimal digits of phi(k) are a permutation of those of k.

1, 21, 63, 291, 502, 2518, 2817, 2991, 4435, 5229, 5367, 5637, 6102, 6174, 6543, 6822, 7236, 7422, 8022, 8541, 8982, 17631, 18231, 18261, 20301, 20518, 20617, 21058, 22471, 22851, 25196, 25918, 27615, 29817, 34816, 35683, 43218, 44305

Offset: 1

Giovanni Resta, Feb 06 2006

Contains A069215 and A113781; is itself a subsequence of A082060. - M. F. Hasler, Nov 28 2007

There is some m > 1 such that a(n) > m*n for all n > 1. This follows from the positive density of numbers n such that n/phi(n) > 10. - Charles R Greathouse IV, Sep 07 2012

			phi(20301) = 13200, phi(6543) = 4356.

V. Raman, Table of n, a(n) for n = 1..10000

Cf. A069215, A113781, A082060, A115920, A114065, A175795.

Select[Range[45000],Sort[IntegerDigits[EulerPhi[#]]]==Sort[IntegerDigits[#]]&] (* Harvey P. Dale, Jul 25 2018 *)

for(n=1,10^5,if(vecsort(Vecsmall(Str(n)))==vecsort(Vecsmall(Str(eulerphi(n)))),print1(n", "))) \\ M. F. Hasler, Nov 28 2007

from sympy import totient
A115921_list = [n for n in range(1,10**4) if sorted(str(totient(n))) == sorted(str(n))] # Chai Wah Wu, Dec 13 2015

Edited by M. F. Hasler, Nov 28 2007

A113781 Numbers k such that the representation of phi(k) is a cyclic permutation of that of k, in base 10.

Original entry on oeis.org

1, 21, 63, 502, 4435, 5229, 5637, 6822, 8022, 35683, 98802, 176481, 210526, 421052, 442881, 480249, 529443, 544435, 640170, 842104, 920262, 976482, 7390422, 21251221, 28934019, 36174255, 36563587, 51804709, 59963997, 60550457

Offset: 1

Giovanni Resta, Jan 26 2006

This is a subsequence of A115921, which in turn is a subsequence of A082060. - M. F. Hasler, Nov 28 2007

			phi(442881) = 288144.

Cf. A000010, A115921, A082060.

lst = {}; Do[s = ToString@n; d = ToString@EulerPhi@n; If[StringLength@d == StringLength@n && {}!= StringPosition[s<>s, d], AppendTo[lst, n]], {n, 10^6}]; lst
lst = {}; Do[s = ToString(AT)n; d = ToString(AT)EulerPhi(AT)n; If[StringLength(AT)d == StringLength(AT)n && {}!= StringPosition[s<>s, d], AppendTo[lst, n]], {n, 10^6}]; lst (* M. F. Hasler, Nov 28 2007 *)

a(24)-a(30) from Donovan Johnson, Aug 27 2010

A243356 Numbers n such that n and phi(n) have no common digits.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 22, 24, 27, 30, 32, 33, 34, 35, 36, 39, 40, 44, 46, 48, 51, 54, 55, 56, 57, 62, 64, 65, 66, 68, 69, 70, 74, 75, 77, 78, 80, 81, 82, 85, 86, 87, 88, 90, 91, 92, 93, 95, 96, 98, 99, 105, 106, 108, 111, 112

Offset: 1

Colin Barker, Jun 03 2014

			108 is in the sequence because phi(108) = 36, which has no digits in common with 108.

Colin Barker, Table of n, a(n) for n = 1..3000

Cf. A000010, A082060.

Select[Range[200],Intersection[IntegerDigits[#],IntegerDigits[EulerPhi[#]]]=={}&] (* Harvey P. Dale, Feb 19 2024 *)

s=[]; for(n=1, 300, if(setintersect(vecsort(digits(n),,8), vecsort(digits(eulerphi(n)),,8))==[], s=concat(s, n))); s

cp's OEIS Frontend

A115921 Numbers k such that the decimal digits of phi(k) are a permutation of those of k.

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A113781 Numbers k such that the representation of phi(k) is a cyclic permutation of that of k, in base 10.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions

A243356 Numbers n such that n and phi(n) have no common digits.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI