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A076377 Numbers k such that k, 2*k, 4*k and 8*k are balanced numbers (A020492). 2
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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A165382 A051015 A221449 * A165374 A024198 A027788
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 15 2002
EXTENSIONS
Missing term added by Donovan Johnson, Mar 03 2013
STATUS
approved

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Last modified July 20 20:50 EDT 2024. Contains 374459 sequences. (Running on oeis4.)