A140173 Numbers k such that sigma(k) = phi(k)*(sum of the digits of k).

1, 6, 3720, 25080, 237000, 353430, 1201560, 1402440, 2104440, 2147040, 4140360, 22007160, 60035220, 104370420, 110095020, 136222020, 402500280, 2203551000, 2223003120, 8720021310, 35590401000, 110232105060, 116046010080, 212062116000, 440401221000, 2181301242120

Offset: 1

Author

Farideh Firoozbakht, May 15 2008

Keywords

• base
• nonn

Comments

Is it true that 10 divides all multi-digit terms of the sequence?

Examples

			sigma(237000) = phi(237000)*(2+3+7+0+0+0).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..36 (calculated using data from _Jud McCranie_)

Crossrefs

Subsequence of A020492.

Cf. A140174.

Programs

Mathematica

Select[Range[10^6],DivisorSigma[1,#]==EulerPhi[#]*DigitSum[#]&] (* James C. McMahon, Jul 06 2025 *)

Extensions

a(13)-a(19) from Sean A. Irvine, Sep 23 2009

a(20)-a(25) from Donovan Johnson, Mar 06 2012

a(26) from Amiram Eldar, Dec 04 2019, using data from Jud McCranie