A292571
Lucas-Carmichael numbers whose Dedekind psi value is a square.
Original entry on oeis.org
935, 31535, 76751, 1707839, 3106799, 11141999, 24685199, 43383167, 83618639, 151524071, 161841239, 189099039, 212133599, 213884999, 219155615, 233743319, 241485839, 271038599, 287432495, 338340239, 353107799, 624840479, 660423455, 945236159, 1171355471
Offset: 1
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psi[n_] := If[n < 1, 0, n*Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]]; s = Import["b006972.txt","Data"][[All,-1]]; Select[s, IntegerQ@Sqrt[psi@#] &]
A292572
Lucas-Carmichael numbers whose Dedekind psi value is a cube.
Original entry on oeis.org
8855, 31535, 73535, 265895, 12676799, 30071327, 86450399, 561645839, 674628479, 741722399, 945066527, 1066699799, 1304305415, 2239506719, 2423951999, 2693338559, 3512071871, 4708417055, 4811496767, 8194093919, 9140299199, 9184665599, 9405512639, 11729537855
Offset: 1
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psi[n_] := If[n < 1, 0, n*Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]]; s = Import["b006972.txt","Data"][[All,-1]];Select[s, IntegerQ@Power[psi@#, 1/3] &]
A290805
Least Carmichael number whose Euler totient function value is an n-th power.
Original entry on oeis.org
561, 1729, 63973, 1729, 367939585, 63973, 294409, 232289960085001, 11570858964626401, 79939760257, 509033161, 611559276803883001, 13079177569, 27685385948423487745, 26979791457662785, 287290964059686145, 13046319747121261903830001, 7847507962539316696504321, 993942550111105, 6280552422566791778305, 24283361157780097, 759608966313690599499265, 6657107145346817668085761, 283219223388059484626764342346640001
Offset: 1
phi(1729) = 36^2 = 6^4 while phi(561) and phi(1105) are not perfect powers, therefore a(2) = a(4) = 1729.
Terms up to a(13) were calculated using Pinch's tables of Carmichael numbers.
Showing 1-3 of 3 results.
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