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A357015
Nonsquarefree numbers whose sum of exponential divisors (A051377) is odd.
2
81, 405, 567, 625, 891, 1053, 1377, 1539, 1863, 1875, 2349, 2401, 2511, 2835, 2997, 3321, 3483, 3807, 4293, 4375, 4455, 4779, 4941, 5265, 5427, 5751, 5913, 6237, 6399, 6723, 6875, 6885, 7203, 7209, 7371, 7695, 7857, 8125, 8181, 8343, 8667, 8829, 9153, 9315, 9639
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
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
Intersection of A013929 and A357014.
Sequence in context: A008848 A237182 A237176 * A102741 A253495 A253456
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 09 2022
STATUS
approved