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

Author

Amiram Eldar, Apr 08 2020

Keywords

• nonn

Comments

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

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.

Crossrefs

Subsequence of A001274.

Cf. A000010, A173557, A333874.

Programs

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