A078557 Squarefree balanced numbers (i.e., squarefree members of A020492).

1, 2, 3, 6, 14, 15, 30, 35, 42, 70, 78, 105, 190, 210, 357, 418, 570, 714, 910, 1045, 1254, 2090, 2730, 3135, 4522, 4674, 5278, 6270, 10659, 12441, 13566, 14630, 15834, 16770, 20026, 21318, 23374, 24871, 24882, 24969, 25070, 25714, 27170, 29029, 33915, 35074

Offset: 1

Author

Labos Elemer, Dec 06 2002

Keywords

• nonn

Examples

			210 = 2*3*5*7, sigma(210) = 576, phi(210) = 48, 576/48 = 12.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A005117 and A020492.

Programs

Mathematica

Do[s=DivisorSigma[1, n]/EulerPhi[n]; If[IntegerQ[s]&&!Equal[MoebiusMu[n], 0], k=k+1; Print[n]], {n, 1, 2100000}]

PARI

isok(k) = {my(f = factor(k)); issquarefree(f) && denominator(prod(i = 1, #f~, (f[i, 1]+1)/(f[i, 1]-1))) == 1;} \\ Amiram Eldar, Feb 24 2025