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

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

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