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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).
1
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
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.
Sequence in context: A210133 A216700 A234411 * A092378 A034634 A014497
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 08 2024
STATUS
approved