A357014 Numbers whose sum of exponential divisors (A051377) is odd.

1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 29, 31, 33, 35, 37, 39, 41, 43, 47, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 101, 103, 105, 107, 109, 111, 113, 115, 119, 123, 127, 129, 131, 133, 137, 139, 141, 143, 145, 149

Offset: 1

Author

Amiram Eldar, Sep 09 2022

Keywords

• nonn

Comments

Includes all the odd squarefree numbers (A056911). First differs from this sequence at n = 34.

Equivalently, the odd terms of A197680, i.e., odd numbers with an odd number of exponential divisors (A049419).

The asymptotic density of this sequence is 0.409797... (A357017).

Examples

			1 is a term since A051377(1) = 1 is odd.
3 is a term since A051377(3) = 3 is odd.
		

Links

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

Crossrefs

Cf. A049419, A051377, A357017.

Subsequence of A197680.

Subsequences: A056911, A357015.

Similar sequences: A000079 (numbers with an odd sum of unitary divisors), A028982 (numbers with an odd sum of divisors).

Programs

Mathematica

f[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[150], OddQ[esigma[#]] &]