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Numbers k such that the number of divisors of k divides the number of divisors of the totient of k.
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%I #30 Jan 31 2025 04:21:53

%S 1,3,7,11,13,14,15,19,22,23,25,28,29,31,35,39,41,43,44,46,47,50,53,55,

%T 56,59,61,62,67,68,70,71,73,77,78,79,82,83,86,87,88,89,91,92,93,94,95,

%U 97,99,103,107,109,110,111,112,113,115,117,118,119,122,124,127,129,131

%N Numbers k such that the number of divisors of k divides the number of divisors of the totient of k.

%H Amiram Eldar, <a href="/A062823/b062823.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1001 from Harry J. Smith)

%e For k = {3,11,29}, phi(k) = {2,10,28}, d(phi(k)) = {2,4,6}, d(k) = 2, quotient = {1,2,3}.

%t Select[Range@ 132, Mod @@ DivisorSigma[0, {EulerPhi@ #, #}] == 0 &] (* _Michael De Vlieger_, Jun 29 2018 *)

%o (PARI) select(m->frac(numdiv(eulerphi(m))/numdiv(m)) == 0, [1..500]) \\ _Harry J. Smith_, Aug 11 2009

%o (PARI) isok(k) = {my(f = factor(k)); !(numdiv(eulerphi(f)) % numdiv(f));} \\ _Amiram Eldar_, Jan 31 2025

%Y Cf. A000005, A000010, A062821.

%K nonn,changed

%O 1,2

%A _Labos Elemer_, Jul 20 2001

%E Incorrect formula deleted by _Jon E. Schoenfield_, Jul 02 2018

%E Offset corrected by _Amiram Eldar_, Jan 31 2025