A381546 Numbers with an odd number of abundant divisors.

12, 18, 20, 30, 36, 42, 48, 56, 66, 70, 72, 78, 80, 84, 88, 90, 102, 104, 108, 114, 120, 126, 132, 138, 140, 144, 156, 162, 174, 186, 192, 196, 198, 204, 222, 224, 228, 234, 246, 252, 258, 270, 272, 276, 282, 288, 300, 304, 306, 308, 318, 320, 324, 330, 336, 342, 348

Offset

1,1

Comments

Numbers k such that A080224(k) is odd.

The primitive abundant numbers (A091191) are all terms of this sequence since A080224(A091191(n)) = 1 for all n.

Links

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

Example

12 is a term since it has only one abundant divisor, 12 itself.
36 is a term since it has 3 abundant divisors, 12, 18 and 36.
72 is a term since it has 5 abundant divisors, 12, 18, 24, 36 and 72.

Mathematica

q[n_] := OddQ[DivisorSum[n, 1 &, DivisorSigma[-1, #] > 2 &]]; Select[Range[350], q]

Prog

(PARI) isok(k) = sumdiv(k, d, (sigma(d, -1) > 2)) % 2;

Crossrefs

Cf. A080224.

Subsequence of A005101.

Subsequences: A091191, A381547, A381548, A381549.

Sequence in context: A054753 A098899 A098770 * A333928 A357695 A192819

Adjacent sequences: A381540 A381541 A381545 * A381547 A381548 A381549

Keyword

nonn,easy

Author

Amiram Eldar, Feb 26 2025

Status

approved