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

%I #23 Dec 04 2019 09:59:49

%S 105,1485,3135,35343,39105,71145,74613,87087,124605,150195,175305,

%T 192855,263055,413655,421005,697851,930699,1404765,1873485,2471931,

%U 2576115,2965599,3281265,3398625,3937635,4172259,4532625,4589949,4975965,5218521,5474115

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

%C 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.

%C 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

%H Amiram Eldar, <a href="/A076377/b076377.txt">Table of n, a(n) for n = 1..10000</a> (calculated using data from Jud McCranie, terms 1..1000 from Donovan Johnson)

%t 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}]

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

%K nonn

%O 1,1

%A _Labos Elemer_, Oct 15 2002

%E Missing term added by _Donovan Johnson_, Mar 03 2013