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A328275 Numbers m such that phi(m) = rad(m)^4, where phi is the Euler totient function (A000010) and rad is the squarefree kernel function (A007947). 2
1, 32, 3888, 25000, 2839714, 3037500, 10890936, 120298932, 402627500, 534837384, 7489147356, 8508543750, 48919241250, 111945866022, 336977358354, 417841706250, 553904623764, 1498168652148, 2627525125250, 2761526809032, 2898701538750, 7978057537338, 16548448068126, 20978349935382 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

De Koninck et al. showed that there are 85 terms in this sequence, yet a(6) = 3037500 was missing in their paper. With a(6), it was verified numerically that the first 38 terms (terms below 10^18) are correct.

LINKS

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

Jean-Marie De Koninck, Florian Luca and A. Sankaranarayanan, Positive integers whose Euler function is a power of their kernel function, Rocky Mountain Journal of Mathematics, Vol. 36, No. 1 (2006), pp. 81-96, alternative link.

EXAMPLE

32 is in the sequence since phi(32) = 16, rad(32) = 2 and 16 = 2^4.

MATHEMATICA

rad[n_] := Times @@ First /@ FactorInteger[n]; aQ[n_] := EulerPhi[n] == rad[n]^4; Select[Range[3*10^6], aQ]

PROG

(PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947

isok(m) = eulerphi(m) == rad(m)^4; \\ Michel Marcus, Oct 15 2019

CROSSREFS

Cf. A000010, A007947, A105261, A211413, A328274, A328276.

Sequence in context: A222053 A264126 A304401 * A291829 A248075 A248000

Adjacent sequences:  A328272 A328273 A328274 * A328276 A328277 A328278

KEYWORD

nonn,fini

AUTHOR

Amiram Eldar, Oct 10 2019

EXTENSIONS

a(6) = 3037500 from Marius A. Burtea, Oct 11 2019

STATUS

approved

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Last modified September 18 05:40 EDT 2021. Contains 347509 sequences. (Running on oeis4.)