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A385743 Numbers k such that A384247(k) = A384247(k+1).

%I A385743 #8 Jul 12 2025 18:50:15
%S A385743 1,20,27,35,63,64,104,143,194,208,740,836,1220,1299,1419,1803,1892,
%T A385743 2625,3255,3705,3716,3843,4096,5184,5186,5635,5695,7868,10659,13365,
%U A385743 16904,17948,18507,18914,21007,22935,25388,25545,27675,30380,31599,32304,32864,34595
%N A385743 Numbers k such that A384247(k) = A384247(k+1).
%C A385743 63 is the only number k below 10^11 such that A384247(k) = A384247(k+1) = A384247(k+2). Are there any other such terms?
%H A385743 Amiram Eldar, <a href="/A385743/b385743.txt">Table of n, a(n) for n = 1..4006</a> (terms below 10^11)
%e A385743 1 is a term since A384247(1) = A384247(2) = 1.
%e A385743 20 is a term since A384247(20) = A384247(21) = 12.
%t A385743 f[p_, e_] := p^e*(1 - 1/p^(2^(IntegerExponent[e, 2]))); iphi[1] = 1; iphi[n_] := iphi[n] = Times @@ f @@@ FactorInteger[n]; Select[Range[35000], iphi[#] == iphi[# + 1] &]
%o A385743 (PARI) iphi(n) = {my(f = factor(n)); n * prod(i = 1, #f~, (1 - 1/f[i, 1]^(1 << valuation(f[i, 2], 2)))); }
%o A385743 list(lim) = {my(s1 = iphi(1), s2); for(k = 2, lim, s2 = iphi(k); if(s1 == s2, print1(k-1, ", ")); s1 = s2);}
%Y A385743 Cf. A384247.
%Y A385743 Similar sequences: A001274, A287055, A293184, A301866, A326403, A349307.
%K A385743 nonn
%O A385743 1,2
%A A385743 _Amiram Eldar_, Jul 08 2025