A115921 - OEIS

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

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OFFSET

1,2

COMMENTS

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

LINKS

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

(Python)

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

CROSSREFS