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

1,2

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Intersection of A005117 and A020492.

Sequence in context: A258077 A121556 A123041 * A005537 A306600 A282351

Adjacent sequences: A078554 A078555 A078556 * A078558 A078559 A078560

Keyword

nonn

Author

Labos Elemer, Dec 06 2002

Status

approved