A381547 Odd numbers with an odd number of abundant divisors.

945, 1575, 2205, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615, 6825, 7245, 7425, 8085, 8415, 8505, 8925, 9135, 9555, 9765, 10395, 11025, 11655, 12285, 12705, 12915, 13545, 14175, 14805, 15015, 16065, 16695, 17955, 18585, 19215, 19635, 19845, 21105, 21735, 21945

Offset: 1

Author

Amiram Eldar, Feb 26 2025

Keywords

• nonn
• easy

Comments

Odd numbers k such that A080224(k) is odd.

Also, odd numbers with an odd sum of abundant divisors.

The odd primitive abundant numbers (A006038) are all terms of this sequence since A080224(A006038(n)) = 1 for all n.

Examples

			945 is a term since it is odd, and it has only one abundant divisor, 945 itself.
4725 is a term since it is odd, and it has 3 abundant divisors, 945, 1575 and 4725.
14175 is a term since it is odd, and it has 5 abundant divisors, 945, 1575, 2835, 4725 and 14175.
		

Links

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

Crossrefs

Cf. A080224, A187795.

Intersection of A005408 and A381546.

Subsequence of A005231.

Subsequences: A006038, A381548, A381549.

Programs

Mathematica

q[n_] := OddQ[DivisorSum[n, 1 &, DivisorSigma[-1, #] > 2 &]]; Select[Range[1, 22000, 2], q]

PARI

isok(k) = if(k % 2, sumdiv(k, d, (sigma(d, -1) > 2)) % 2, 0);