cp's OEIS Frontend

A036798 Odd numbers m such that there exists an even number k < m with phi(k) = phi(m).

%I A036798 #31 Nov 21 2024 06:13:23
%S A036798 105,165,195,315,495,525,585,735,825,945,975,1155,1365,1485,1575,1755,
%T A036798 1785,1815,1995,2145,2205,2415,2475,2535,2625,2805,2835,2925,3003,
%U A036798 3045,3135,3255,3315,3465,3675,3705,3795,3885,3927,4095,4125,4305,4389,4455
%N A036798 Odd numbers m such that there exists an even number k < m with phi(k) = phi(m).
%C A036798 These numbers m appear to satisfy cototient(m) > totient(m) or 2*phi(m) < m; they seem to be the missing terms mentioned in A067800. - _Labos Elemer_, May 08 2003
%C A036798 All elements in this sequence must have 2*phi(m) < m, but not the reverse. See A118700. - _Franklin T. Adams-Watters_, May 21 2006
%C A036798 The numbers of terms that do not exceed 10^k, for k = 3, 4, ..., are 11, 108, 1139, 11036, 111796, ... . Apparently, the asymptotic density of this sequence exists and equals 0.011... . - _Amiram Eldar_, Nov 21 2024
%H A036798 Robert Israel, <a href="/A036798/b036798.txt">Table of n, a(n) for n = 1..10000</a>
%H A036798 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%p A036798 N:= 10^4: # to get all terms <= N
%p A036798 PhiE:= map(numtheory:-phi, [seq(i,i=2..N,2)]):
%p A036798 A:= NULL:
%p A036798 for n from 1 to N by 2 do
%p A036798 t:= numtheory:-phi(n);
%p A036798 if 2*t < n and member(t, PhiE[1..(n-1)/2]) then A:= A,n fi;
%p A036798 od:
%p A036798 A; # _Robert Israel_, Jan 06 2017
%o A036798 (PARI) is(m) = m%2 && #select(k -> !(k%2) && k < m, invphi(eulerphi(m))) > 0; \\ _Amiram Eldar_, Nov 21 2024, using _Max Alekseyev_'s invphi.gp
%Y A036798 Cf. A000010, A067800, A083254.
%Y A036798 Cf. A091495 (Odd, squarefree n such that n/phi(n) > 2).
%Y A036798 Cf. A118700, A119434.
%K A036798 nonn
%O A036798 1,1
%A A036798 _David W. Wilson_