A067543 - OEIS

A067543

Numbers k such that phi(k*(k+1)*(k+2)*(k+3)/4!)/phi(k*(k+1)*(k+2)/3!) is not an integer where phi(n) = A000010(n) is the Euler totient function.

6, 8, 16, 24, 40, 46, 54, 56, 64, 78, 80, 104, 118, 126, 128, 136, 144, 160, 176, 198, 208, 224, 240, 248, 280, 304, 328, 344, 358, 360, 376, 414, 416, 440, 464, 486, 488, 496, 520, 526, 544, 560, 568, 584, 616, 630, 640, 656, 680, 688, 726, 736, 784

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OFFSET

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

MATHEMATICA

q[k_] := !Divisible[EulerPhi[k*(k+1)*(k+2)*(k+3)/24], EulerPhi[k*(k+1)*(k+2)/6]]; Select[Range[1000], q] (* Amiram Eldar, May 09 2025 *)

PROG

(PARI) isok(k) = denominator(eulerphi(k*(k+1)*(k+2)*(k+3)/4!)/eulerphi(k*(k+1)*(k+2)/3!)) != 1; \\ Michel Marcus, Dec 19 2023

CROSSREFS

Cf. A000010 (phi).

Sequence in context: A315940 A383420 A048228 * A006583 A011989 A270821