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A287055
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Numbers n such that uphi(n) = uphi(n+1), where uphi(n) is the unitary totient function (A047994).
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10
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Chai Wah Wu, Table of n, a(n) for n = 1..2198 (terms 1..207 from Amiram Eldar)
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EXAMPLE
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uphi(20) = uphi(21) = 12, thus 20 is in the sequence.
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MATHEMATICA
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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
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PROG
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(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
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CROSSREFS
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Cf. A001274, A047994.
Sequence in context: A254363 A229356 A048066 * A326403 A335251 A135801
Adjacent sequences: A287052 A287053 A287054 * A287056 A287057 A287058
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KEYWORD
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nonn
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AUTHOR
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Amiram Eldar, May 18 2017
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STATUS
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approved
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