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A287055 Numbers n such that uphi(n) = uphi(n+1), where uphi(n) is the unitary totient function (A047994).

%I A287055 #23 Oct 01 2021 10:25:08
%S A287055 1,20,35,143,194,208,740,1119,1220,1299,1419,1803,1892,2232,2623,3705,
%T A287055 3716,3843,4995,5031,5183,5186,5635,7868,10659,17948,18507,18914,
%U A287055 21007,23616,25388,25545,30380,30744,31599,32304,34595,37820,38024,47067,60767,70394
%N A287055 Numbers n such that uphi(n) = uphi(n+1), where uphi(n) is the unitary totient function (A047994).
%C A287055 The unitary version of A001274 (phi(n) = phi(n+1)). The first terms that are common to both sequences are: 1, 194, 3705, 5186, 25545, 388245, 1659585, 2200694, 2521694, 2619705, 3289934, 4002405, 5781434, 6245546, 6372794, 8338394.
%H A287055 Chai Wah Wu, <a href="/A287055/b287055.txt">Table of n, a(n) for n = 1..2198</a> (terms 1..207 from Amiram Eldar)
%e A287055 uphi(20) = uphi(21) = 12, thus 20 is in the sequence.
%t A287055 uphi[n_] := If[n==1,1,(Times @@ (Table[#[[1]]^#[[2]] - 1, {1}] & /@ FactorInteger[n]))[[1]]]; a={}; u1=0; For[k=0, k<10^5, k++; u2=uphi[k]; If[u1==u2, a = AppendTo[a, k-1]]; u1=u2]; a
%o A287055 (PARI) uphi(n) = my(f = factor(n)); prod(i=1, #f~, f[i,1]^f[i,2]-1);
%o A287055 isok(n) = uphi(n+1) == uphi(n); \\ _Michel Marcus_, May 20 2017
%o A287055 (Python)
%o A287055 from math import prod
%o A287055 from sympy import factorint
%o A287055 A287055_list, a, n = [], 1, 1
%o A287055 while n < 10**5:
%o A287055     b = prod(p**e-1 for p, e in factorint(n+1).items())
%o A287055     if a == b:
%o A287055         A287055_list.append(n)
%o A287055     a, n = b, n+1 # _Chai Wah Wu_, Sep 24 2021
%Y A287055 Cf. A001274, A047994.
%K A287055 nonn
%O A287055 1,2
%A A287055 _Amiram Eldar_, May 18 2017