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

1,1

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.

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A080224, A187795.

Intersection of A005408 and A381546.

Subsequence of A005231.

Subsequences: A006038, A381548, A381549.

Sequence in context: A174865 A174535 A243104 * A006038 A287646 A316116

Adjacent sequences: A381541 A381545 A381546 * A381548 A381549 A381550

Keyword

nonn,easy,new

Author

Amiram Eldar, Feb 26 2025

Status

approved