A373530 Numbers k such that k, k+1 and k+2 all have at least three divisors with the same value of the Euler totient function (A000010).

14052608, 83025998, 87703714, 93978520, 117345150, 163338174, 213589088, 218539880, 294321950, 369698434, 401177798, 463425920, 470217824, 497434040, 529524918, 539318438, 554556078, 559474838, 581302358, 584754848, 608842934, 612448640, 617445814, 625591966

Offset

1,1

Comments

Numbers k such that k, k+1 and k+2 are all in A359565.

There must be 3 or more divisors of k that have the same Euler totient value, and ditto for k+1 and k+2, but those values may differ as among k, k+1, and k+2. - Harvey P. Dale, Sep 01 2024

Links

Table of n, a(n) for n=1..24.

Mathematica

q[n_] := Max[Tally[EulerPhi[Divisors[n]]][[;; , 2]]] > 2; seq[kmax_] := Module[{s = {}, q1 = 0, q2 = 0, q3}, Do[q3 = q[k]; If[q1 && q2 && q3, AppendTo[s, k-2]]; q1=q2; q2=q3, {k, 3, kmax}]; s]; seq[10^8]
SequencePosition[Table[If[Max[Tally[EulerPhi[Divisors[n]]][[;; , 2]]]>2, 1, 0], {n, 88*10^6}], {1, 1, 1}] [[;; , 1]] (* The program generates the first 3 terms of the sequence. *) (* Harvey P. Dale, Sep 01 2024 *)

Prog

(PARI) is(k) = vecmax(matreduce(apply(x->eulerphi(x), divisors(k)))[, 2]) > 2;
lista(kmax) = {my(q1 = 0, q2 = 0, q3); for(k = 3, kmax, q3 = is(k); if(q1 && q2 && q3, print1(k-2, ", ")); q1 = q2; q2 = q3); }

Crossrefs

Subsequence of A359565 and A373529.

Cf. A000010, A102190.

Sequence in context: A210133 A216700 A234411 * A092378 A034634 A014497

Adjacent sequences: A373527 A373528 A373529 * A373531 A373532 A373533

Keyword

nonn,changed

Author

Amiram Eldar, Jun 08 2024

Status

approved