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A357014
Numbers whose sum of exponential divisors (A051377) is odd.
4
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
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 09 2022
STATUS
approved