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Numbers k such that k and phi(k) have the same number of divisors.
4

%I #39 Mar 23 2024 20:32:57

%S 1,3,14,15,22,28,44,46,50,56,68,70,78,88,92,94,110,112,118,166,174,

%T 176,184,188,198,214,224,228,230,234,236,255,260,294,306,318,332,334,

%U 342,352,358,368,376,414,428,448,454,462,470,472,492,500,526,550,580,590

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

%C 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

%H G. C. Greubel, <a href="/A070418/b070418.txt">Table of n, a(n) for n = 1..8407</a> (for values up to 500000)

%H Djamel Bellaouar, Abdelmadjid Boudaoud and Rafael Jakimczuk, <a href="https://doi.org/10.1515/ms-2023-0045">Notes on the equation d(n) = d(phi(n)) and related inequalities</a>, Math. Slovaca 73 (2023), no. 3, 613-632.

%t Select[Range[600],DivisorSigma[0,#]==DivisorSigma[0,EulerPhi[#]]&] (* _Harvey P. Dale_, Sep 04 2015 *)

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

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

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, May 12 2002