A357015 Nonsquarefree numbers whose sum of exponential divisors (A051377) is odd.

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

Author

Amiram Eldar, Sep 09 2022

Keywords

• nonn

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... .

Examples

			81 = 3^4 is a term since it is not squarefree and A051377(81) = 93 is odd.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A013929 and A357014.

Cf. A005117, A051377, A056911, A185199.

Programs

Mathematica

f[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^4], ! SquareFreeQ[#] && OddQ[esigma[#]] &]