Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Nov 14 2021 07:48:14
%S 80,135,296,343,375,624,728,1160,1431,1592,1624,2240,2295,2456,2511,
%T 2624,2727,2888,3429,3591,3624,3752,3992,4023,4184,4671,4887,4913,
%U 5048,5144,5264,5319,5480,5696,6183,6344,6375,6591,6615,6776,6858,6859,7479,7624,7640
%N Numbers k such that A321167(k) = A321167(k+1) > 1.
%C Without the restriction that A321167(k) > 1, all the terms of A340152 would be in this sequence.
%C 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, ...
%H Amiram Eldar, <a href="/A349308/b349308.txt">Table of n, a(n) for n = 1..10000</a>
%e 80 is a term since A321167(80) = A321167(81) = 3.
%t 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 &]
%Y Cf. A321167, A340152.
%Y Subsequence of A068140.
%Y Similar sequences: A001274, A287055, A293184, A326403, A349307.
%K nonn
%O 1,1
%A _Amiram Eldar_, Nov 14 2021