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

1,1

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

Intersection of A013929 and A357014.

Cf. A005117, A051377, A056911, A185199.

Sequence in context: A008848 A237182 A237176 * A102741 A253495 A253456

Adjacent sequences: A357012 A357013 A357014 * A357016 A357017 A357018

Keyword

nonn

Author

Amiram Eldar, Sep 09 2022

Status

approved