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A335289 Nonsquarefree numbers that are both balanced numbers (A020492) and unitary balanced numbers (A335288). 2
1492260, 1741740, 2369640, 7192260, 83445180, 91798980, 104370420, 125214180, 141996120, 148532076, 162910980, 171175788, 196899780, 199793412, 201246660, 229849620, 297085860, 298993140, 398023080, 442859940, 540201480, 548305740, 796792920, 801375660, 835975140 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The squarefree balanced numbers (A078557) are also unitary balanced numbers (A335288), since all the divisors of squarefree numbers are unitary, and thus if k is squarefree, then sigma(k) = usigma(k) and phi(k) = uphi(k).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..4045 (calculated using data from Jud McCranie)
EXAMPLE
1492260 is a term since sigma(1492260)/phi(1492260) = 5806080/276480 = 21 is an integer, usigma(1492260)/uphi(1492260) = 4147200/414720 = 10 is an integer, and 1492260 is not squarefree since it is divisible by 4 = 2^2.
MATHEMATICA
f1[1, 1] = 1; f1[p_, e_] := (p^(e+1) - 1)/p^(e-1)/(p-1)^2; f2[1, 1] = 1; f2[p_, e_] := (p^e + 1)/(p^e -1); balQ[n_] := And @@ IntegerQ /@ Times@@({f1[#1, #2], f2[#1, #2]}& @@@ FactorInteger[n]); Select[Range[3*10^6], !SquareFreeQ[#] && balQ[#] &]
CROSSREFS
Intersection of A013929, A020492 and A335288.
Cf. A000010 (phi), A000203 (sigma), A047994 (uphi), A034448 (usigma), A078557.
Sequence in context: A126175 A128837 A297881 * A228761 A206060 A251973
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 30 2020
STATUS
approved

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Last modified July 23 03:10 EDT 2024. Contains 374544 sequences. (Running on oeis4.)