A076377 Numbers k such that k, 2*k, 4*k and 8*k are balanced numbers (A020492).

105, 1485, 3135, 35343, 39105, 71145, 74613, 87087, 124605, 150195, 175305, 192855, 263055, 413655, 421005, 697851, 930699, 1404765, 1873485, 2471931, 2576115, 2965599, 3281265, 3398625, 3937635, 4172259, 4532625, 4589949, 4975965, 5218521, 5474115

Offset: 1

Author

Labos Elemer, Oct 15 2002

Keywords

• nonn

Comments

The quotients q = Sigma(u)/phi(u) for u = {n, 2n, 4n, 8n} are integers and for all terms, and equal 4, 12, 14, 15 respectively. For u = 16n, q = 31/2, i.e. no integer was found for u < 6000000.

The comment above is true for terms up to a(238) and true for 985 of the first 1000 terms. - Donovan Johnson, Mar 03 2013

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Jud McCranie, terms 1..1000 from Donovan Johnson)

Crossrefs

Cf. A000010, A000203, A055234, A020492, A076375, A076376.

Programs

Mathematica

f[x_] := DivisorSigma[1, x]/EulerPhi[x] Do[s=f[n]; s1=f[2*n]; s2=f[4*n]; s3=f[8*n] If[IntegerQ[s]&&IntegerQ[s1]&&IntegerQ[s2]&& IntegerQ[s3], Print[n]], {n, 1, 10000000}]

Extensions

Missing term added by Donovan Johnson, Mar 03 2013