A349308 Numbers k such that A321167(k) = A321167(k+1) > 1.

80, 135, 296, 343, 375, 624, 728, 1160, 1431, 1592, 1624, 2240, 2295, 2456, 2511, 2624, 2727, 2888, 3429, 3591, 3624, 3752, 3992, 4023, 4184, 4671, 4887, 4913, 5048, 5144, 5264, 5319, 5480, 5696, 6183, 6344, 6375, 6591, 6615, 6776, 6858, 6859, 7479, 7624, 7640

Offset

1,1

Comments

Without the restriction that A321167(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 6858, 13375, 22625, ...

Links

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

Example

80 is a term since A321167(80) = A321167(81) = 3.

Mathematica

f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; fe[p_, e_] := uphi[e]; euphi[n_] := Times @@ fe @@@ FactorInteger[n]; Select[Range[8000], euphi[#] == euphi[# + 1] > 1 &]

Crossrefs

Cf. A321167, A340152.

Subsequence of A068140.

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

Sequence in context: A068140 A365867 A349307 * A224547 A204648 A202447

Adjacent sequences: A349305 A349306 A349307 * A349309 A349310 A349311

Keyword

nonn

Author

Amiram Eldar, Nov 14 2021

Status

approved