A070418 Numbers k such that k and phi(k) have the same number of divisors.

1, 3, 14, 15, 22, 28, 44, 46, 50, 56, 68, 70, 78, 88, 92, 94, 110, 112, 118, 166, 174, 176, 184, 188, 198, 214, 224, 228, 230, 234, 236, 255, 260, 294, 306, 318, 332, 334, 342, 352, 358, 368, 376, 414, 428, 448, 454, 462, 470, 472, 492, 500, 526, 550, 580, 590

Offset: 1

Author

Benoit Cloitre, May 12 2002

Keywords

• easy
• nonn

Comments

This is an infinite sequence; for example, 2^(m-1)*5^m is in the sequence for all m >= 2. See Bellaouar et al. 2023. - Allen Stenger, Feb 16 2024

Links

• G. C. Greubel, Table of n, a(n) for n = 1..8407 (for values up to 500000)
• Djamel Bellaouar, Abdelmadjid Boudaoud and Rafael Jakimczuk, Notes on the equation d(n) = d(phi(n)) and related inequalities, Math. Slovaca 73 (2023), no. 3, 613-632.

Crossrefs

Cf. A000005, A000010 (phi), A116518 (odd terms).

Programs

Mathematica

Select[Range[600],DivisorSigma[0,#]==DivisorSigma[0,EulerPhi[#]]&] (* Harvey P. Dale, Sep 04 2015 *)

PARI

for(n=1,900,if(numdiv(n)==numdiv(eulerphi(n)),print1(n,",")))