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

1,2

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).

Links

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

Example

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

Mathematica

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

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).

Sequence in context: A305635 A334420 A342144 * A056911 A152955 A235866

Adjacent sequences: A357011 A357012 A357013 * A357015 A357016 A357017

Keyword

nonn

Author

Amiram Eldar, Sep 09 2022

Status

approved