A078540 -id:A078540 - cp's OEIS frontend

A078542 Unbalanced composite numbers.

4, 8, 9, 10, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 32, 33, 34, 36, 38, 39, 40, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 72, 74, 75, 76, 77, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 106, 108

Offset: 1

Labos Elemer, Dec 04 2002

nonn

			46 = 2*23 and sigma(46)/phi(46) = 72/22 is not an integer, so 46 is in the sequence.

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

Cf. A000010, A000203, A020492, A078538, A078539, A078540.

Do[s=DivisorSigma[1, n]/EulerPhi[n]; If[ !IntegerQ[s]&&!PrimeQ[n], Print[n]], {n, 1, 256}]
Select[Range[150],CompositeQ[#]&&!IntegerQ[DivisorSigma[1,#]/ EulerPhi[ #]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 19 2020 *)

lista(nn) = forcomposite(n=1, nn, if (denominator(sigma(n)/eulerphi(n)) != 1, print1(n, ", "))); \\ Michel Marcus, Jul 11 2018

A078543 Balanced refactorable numbers.

Original entry on oeis.org

1, 2, 12, 56, 248, 12192, 28896, 60960, 61344, 66528, 86304, 94944, 129504, 133920, 140448, 182880, 201924, 207264, 242316, 282720, 408672, 416640, 426720, 429408, 604128, 664608, 671760, 776736, 792480, 854496, 862752, 906528

Offset: 1

Labos Elemer, Dec 04 2002

nonn

			n=56: tau(56)=8, sigma(56)=120, phi(56)=24, q1=120/24=5 for balancedness, q2=56/8=7 for refactorability.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Jud McCranie, terms 1..500 from Donovan Johnson)

Intersection of A033950 and A020492.

Cf. A078538, A078539, A078540.

Do[s=DivisorSigma[1, n]/EulerPhi[n]; If[ !IntegerQ[s]&&!PrimeQ[n], Print[n]], {n, 1, 256}]

cp's OEIS Frontend

A078542 Unbalanced composite numbers.

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