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

1,2

Comments

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

Example

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

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

Prog

(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

Crossrefs

Subsequence of A001274.

Cf. A000010, A173557, A333874.

Sequence in context: A205356 A281807 A220160 * A183583 A296893 A045073

Adjacent sequences: A333872 A333873 A333874 * A333876 A333877 A333878

Keyword

nonn

Author

Amiram Eldar, Apr 08 2020

Status

approved