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

Author

Amiram Eldar, Feb 26 2025

Keywords

• nonn
• easy

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A080224.

Subsequence of A005101.

Subsequences: A091191, A381547, A381548, A381549.

Programs

Mathematica

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

PARI

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