OFFSET
1,1
COMMENTS
This sequence is the second subsequence of A326707: squares of composites which have no Brazilian representation with three digits or more.
As tau(m) = 2 * beta(m) + 3, the number of divisors of these squares of composites m is odd with tau(m) >= 5.
The corresponding composites are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 42, ...
EXAMPLE
a(1) = 16: tau(16) = 5 and beta(16) = 1 with 16 = 4^2 = 22_7.
a(3) = 64: tau(64) = 7 and beta(64) = 2 with 64 = 8^2 = 44_15 = 22_31.
a(5) = 100: tau(100) = 9 and beta(100) = 3 with 100 = 10^2 = 55_19 = 44_24 = 22_49.
MATHEMATICA
brazQ[n_, b_] := Length@Union@IntegerDigits[n, b] == 1; beta[n_] := Sum[Boole @ brazQ[n, b], {b, 2, n - 2}]; aQ[n_] := beta[n] == (DivisorSigma[0, n] - 3)/2; Select[Select[Range[75], CompositeQ]^2, aQ] (* Amiram Eldar, Sep 06 2019 *)
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Aug 29 2019
STATUS
approved