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 A287055 Numbers n such that uphi(n) = uphi(n+1), where uphi(n) is the unitary totient function (A047994). 10
 1, 20, 35, 143, 194, 208, 740, 1119, 1220, 1299, 1419, 1803, 1892, 2232, 2623, 3705, 3716, 3843, 4995, 5031, 5183, 5186, 5635, 7868, 10659, 17948, 18507, 18914, 21007, 23616, 25388, 25545, 30380, 30744, 31599, 32304, 34595, 37820, 38024, 47067, 60767, 70394 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Chai Wah Wu, Table of n, a(n) for n = 1..2198 (terms 1..207 from Amiram Eldar) EXAMPLE uphi(20) = uphi(21) = 12, thus 20 is in the sequence. MATHEMATICA 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 PROG (PARI) uphi(n) = my(f = factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2]-1); isok(n) = uphi(n+1) == uphi(n); \\ Michel Marcus, May 20 2017 (Python) from math import prod from sympy import factorint A287055_list, a, n = [], 1, 1 while n < 10**5:     b = prod(p**e-1 for p, e in factorint(n+1).items())     if a == b:         A287055_list.append(n)     a, n = b, n+1 # Chai Wah Wu, Sep 24 2021 CROSSREFS Cf. A001274, A047994. Sequence in context: A254363 A229356 A048066 * A326403 A335251 A135801 Adjacent sequences:  A287052 A287053 A287054 * A287056 A287057 A287058 KEYWORD nonn AUTHOR Amiram Eldar, May 18 2017 STATUS approved

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Last modified May 29 08:14 EDT 2022. Contains 354124 sequences. (Running on oeis4.)