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

1,1

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)

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}]

Crossrefs

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

Sequence in context: A165382 A051015 A221449 * A165374 A024198 A027788

Adjacent sequences: A076374 A076375 A076376 * A076378 A076379 A076380

Keyword

nonn

Author

Labos Elemer, Oct 15 2002

Extensions

Missing term added by Donovan Johnson, Mar 03 2013

Status

approved