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

Author

Amiram Eldar, May 18 2017

Keywords

• nonn

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.

Examples

			uphi(20) = uphi(21) = 12, thus 20 is in the sequence.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..2198 (terms 1..207 from Amiram Eldar)

Crossrefs

Cf. A001274, A047994.

Programs

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

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