A333875 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).
1, 194, 3705, 5186, 25545, 388245, 1659585, 2200694, 2521694, 2619705, 3289934, 3794834, 4002405, 5781434, 6245546, 6372794, 8338394, 12352934, 14144954, 16475414, 22632285, 23553705, 37762394, 40588485, 43834754, 44485454, 59603954, 63298785, 76466985, 81591194
Offset: 1
Keywords
Examples
1 is a term since 1 and 2 are both squarefree and phi(1) = phi(2) = 1.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..1166 (terms below 10^13, calculated from the b-file at A001274)
- Daeyeoul Kim, Umit Sarp, and Sebahattin Ikikardes, Certain combinatoric convolution sums arising from Bernoulli and Euler Polynomials, Miskolc Mathematical Notes, No. 20, Vol. 1 (2019): pp. 311-330.
Programs
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Mathematica
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 -
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
Comments