A333875 - OEIS

%I #11 Apr 09 2020 05:24:42

%S 1,194,3705,5186,25545,388245,1659585,2200694,2521694,2619705,3289934,

%T 3794834,4002405,5781434,6245546,6372794,8338394,12352934,14144954,

%U 16475414,22632285,23553705,37762394,40588485,43834754,44485454,59603954,63298785,76466985,81591194

%N Numbers k such that both k and k+1 are squarefree and phi(k) = phi(k+1), where phi is the Euler totient function (A000010).

%C Numbers k such that A000010(k) = A000010(k+1) = A173557(k) = A173557(k+1).

%H Amiram Eldar, <a href="/A333875/b333875.txt">Table of n, a(n) for n = 1..1166</a> (terms below 10^13, calculated from the b-file at A001274)

%H Daeyeoul Kim, Umit Sarp, and Sebahattin Ikikardes, <a href="http://dx.doi.org/10.18514/MMN.2019.2470">Certain combinatoric convolution sums arising from Bernoulli and Euler Polynomials</a>, Miskolc Mathematical Notes, No. 20, Vol. 1 (2019): pp. 311-330.

%e 1 is a term since 1 and 2 are both squarefree and phi(1) = phi(2) = 1.

%t s = {}; p1 = 1; Do[p2 = If[SquareFreeQ[n], EulerPhi[n], 0]; If[p2 > 0 && p2 == p1, AppendTo[s, n-1]]; p1 = p2, {n, 2, 10^5}]; s

%o (PARI) for(k=1,10^7, if(issquarefree(k), if(issquarefree(k+1), if(eulerphi(k)==eulerphi(k+1),print1(k,", "))))) \\ _Hugo Pfoertner_, Apr 08 2020

%Y Subsequence of A001274.

%Y Cf. A000010, A173557, A333874.

%K nonn

%O 1,2

%A _Amiram Eldar_, Apr 08 2020