A175795 Numbers n such that the digits of sigma(n) are exactly the same (albeit in different order) as the digits of phi(n), in base 10.

1, 65, 207, 1769, 2066, 2771, 3197, 4330, 4587, 4769, 4946, 5067, 6443, 6623, 6989, 7133, 8201, 9263, 11951, 12331, 13243, 16403, 17429, 17441, 21416, 22083, 23161, 24746, 27058, 27945, 28049, 28185, 28451, 29111, 30551, 31439, 32554, 32566, 32849, 33715

Offset: 1

Author

Michel Lagneau, Sep 06 2010

Keywords

• nonn
• base

Examples

			2771 is in the sequence because sigma(2771) = 2952, phi(2771) = 2592
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010 (Euler totient function), A000203 (sigma function), A115920, A115921, A114065.

Programs

Mathematica

okQ[n_] := Module[{idn = IntegerDigits[DivisorSigma[1,n]]}, Sort[idn] == Sort[IntegerDigits[EulerPhi[n]]]]; Select[Range[40000], okQ]

PARI

isok(n) = (de = digits(eulerphi(n))) && (ds = digits(sigma(n))) && (vecsort(de) == vecsort(ds)); \\ Michel Marcus, Dec 13 2015

Python

from sympy import totient, divisor_sigma
A175795_list = [n for n in range(1,10**4) if sorted(str(divisor_sigma(n))) == sorted(str(totient(n)))] # Chai Wah Wu, Dec 13 2015