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A255199 Numbers k such that mu(k) = mu(phi(k)) where mu(k) is the Möbius function and phi(k) is Euler's totient function. 2
1, 3, 8, 12, 14, 16, 20, 22, 24, 25, 27, 28, 31, 32, 36, 40, 43, 44, 45, 46, 48, 50, 52, 54, 56, 60, 63, 64, 67, 68, 71, 72, 75, 76, 79, 80, 81, 84, 88, 90, 92, 94, 96, 99, 100, 103, 104, 108, 112, 116, 117, 118, 120, 124, 125, 126, 128, 131, 132, 135, 136, 139 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If k and phi(k) are both not squarefree then k is in the list.

A prime p is in the list if p - 1 is squarefree and bigomega(p - 1) = A001222(p - 1) is odd.

It follows that the subsequence of primes is A078330. - Bernard Schott, Apr 03 2021

LINKS

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

EXAMPLE

8 is in the list since mu(8) = 0 and mu(phi(8)) = mu(4) = 0.

7 is not in the list since mu(7) = -1 and mu(phi(7)) = mu(6) = 1.

MATHEMATICA

Select[Range[200], MoebiusMu[#] == MoebiusMu[EulerPhi[#]] &] (* Alonso del Arte, Feb 16 2015 *)

PROG

(Sage)

[n for n in [1..1000] if moebius(n)==moebius(euler_phi(n))]

(PARI) for(n=1, 140, if(moebius(n) == moebius(eulerphi(n)), print1(n, ", "))) \\  Indranil Ghosh, Mar 11 2017

CROSSREFS

Cf. A000010, A008683, A033631, A013929, A078330.

Sequence in context: A288865 A331069 A161517 * A280239 A344345 A310284

Adjacent sequences:  A255196 A255197 A255198 * A255200 A255201 A255202

KEYWORD

nonn

AUTHOR

Tom Edgar, Feb 16 2015

STATUS

approved

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Last modified June 23 12:05 EDT 2021. Contains 345401 sequences. (Running on oeis4.)