OFFSET
1,1
COMMENTS
The squarefree numbers are excluded from this sequence since the sum of the exponential divisors of any squarefree number k is A005117(k) = k, so the sum of the exponential divisors of any odd squarefree number (A056911) is odd.
Equivalently, odd nonsquarefree numbers whose exponents in their prime factorization are squares.
The asymptotic density of this sequence is A357017 - 4/Pi^2 = 0.0045127121... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
81 = 3^4 is a term since it is not squarefree and A051377(81) = 93 is odd.
MATHEMATICA
f[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^4], ! SquareFreeQ[#] && OddQ[esigma[#]] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 09 2022
STATUS
approved