A349308 -id:A349308 - cp's OEIS frontend

A349307 Numbers k such that A072911(k) = A072911(k+1) > 1.

80, 135, 296, 343, 375, 567, 624, 728, 783, 944, 1160, 1431, 1592, 1624, 1647, 1808, 1863, 2024, 2240, 2295, 2456, 2511, 2624, 2727, 2888, 3087, 3320, 3429, 3536, 3591, 3624, 3752, 3992, 4023, 4184, 4239, 4375, 4400, 4455, 4624, 4671, 4887, 4912, 4913, 5048, 5103

Offset: 1

Amiram Eldar, Nov 14 2021

nonn

Without the restriction that A072911(k) > 1, all the terms of A340152 would be in this sequence.

In contrast to A001274, which has only one known pair of consecutive terms (5186 and 5187), this sequence seems to have many pairs of consecutive terms. The smaller members of these pairs are 4912, 5750, 6858, ...

			80 is a term since A072911(80) = A072911(81) = 2.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A072911, A340152.
Subsequence of A068140.
Similar sequences: A001274, A287055, A293184, A326403, A349308.

f[p_, e_] := EulerPhi[e]; ephi[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[5000], ephi[#] == ephi[# + 1] > 1 &]

A349309 Numbers k such that A254926(k) = A254926(k+1).

Original entry on oeis.org

7, 26, 124, 342, 1330, 2196, 12166, 24388, 29790, 79506, 103822, 148876, 205378, 226980, 300762, 357910, 493038, 571786, 1030300, 1092726, 1225042, 2248090, 2685618, 3307948, 3442950, 3869892, 4657462, 5177716, 5735338, 6967870, 7645372, 9393930, 11089566, 11697082

Offset: 1

Amiram Eldar, Nov 14 2021

nonn

			7 is a term since A254926(7) = A254926(8) = 7.

Amiram Eldar, Table of n, a(n) for n = 1..100

Cf. A254926.

Similar sequences: A001274, A287055, A293184, A326403, A336673, A349307, A349308.

f[p_, e_] := If[e < 3, p^e, p^e - p^(e - 3)]; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^6], s[#] == s[# + 1] &]

from math import prod
from itertools import count, islice
from sympy import factorint
def A349309_gen(startvalue=1): # generator of terms >= startvalue
    a = prod(p**e - (p**(e-3) if e >= 3 else 0) for p, e in factorint(max(startvalue,1)).items())
    for k in count(max(startvalue,1)):
        b = prod(p**e - (p**(e-3) if e >= 3 else 0) for p, e in factorint(k+1).items())
        if a == b:
            yield k
        a = b
A349309_list = list(islice(A349309_gen(),10)) # Chai Wah Wu, Jan 24 2022

cp's OEIS Frontend

A349307 Numbers k such that A072911(k) = A072911(k+1) > 1.

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