A326403 - OEIS

A326403

Numbers k such that iphi(k) = iphi(k+1), where iphi(k) is an infinitary analog to the Euler totient function (A091732).

%I #15 Sep 14 2019 16:39:46

%S 1,20,35,143,194,208,740,1220,1299,1419,1803,1892,3705,3716,3843,5186,

%T 5635,7868,10659,13634,13905,17948,18507,18914,18980,21007,25388,

%U 25545,30380,31599,32304,34595,37820,47067,70394,73059,78064,87856,94874,105908,116963

%N Numbers k such that iphi(k) = iphi(k+1), where iphi(k) is an infinitary analog to the Euler totient function (A091732).

%H Amiram Eldar, <a href="/A326403/b326403.txt">Table of n, a(n) for n = 1..1000</a>

%e 20 is in the sequence since iphi(20) = iphi(21) = 12.

%t f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], _?(# == 1 &)])); a[1] = 1; a[n_] := Times @@ (Flatten @(f @@@ FactorInteger[n]) - 1); a1 = 1; s = {}; Do[a2 = a[n]; If[a1 == a2, AppendTo[s, n - 1]]; a1 = a2, {n, 2, 10^5}]; s

%Y Cf. A001274, A091732, A287055, A293184, A301866.

%K nonn

%O 1,2

%A _Amiram Eldar_, Sep 14 2019