A381550 Numbers whose sum of abundant divisors is odd.

945, 1575, 1890, 2205, 3150, 3465, 3780, 4095, 4410, 4725, 5355, 5775, 5985, 6300, 6435, 6615, 6825, 6930, 7245, 7425, 7560, 8085, 8190, 8415, 8505, 8820, 8925, 9135, 9450, 9555, 9765, 10395, 10710, 11025, 11550, 11655, 11970, 12285, 12600, 12705, 12870, 12915

Offset: 1

Author

Amiram Eldar, Feb 26 2025

Keywords

• nonn
• easy

Comments

Numbers k such that A187795(k) is odd.

Numbers whose odd part has an odd number of abundant divisors, i.e., numbers k such that A080224(A000265(k)) is odd.

If m is an odd term then 2^k * m is a term for all k >= 0. Therefore, the primitive terms of this sequence are the odd terms, that are also the odd numbers whose number of abundant divisors is odd (A381547).

Are there two consecutive integers in this sequence? There are none below 10^10.

Examples

			945 is a term since its sum of abundant divisors is 945, which is odd.
4725 is a term since its sum of abundant divisors is 945 + 1575 + 4725 = 7245, which is odd.
		

Links

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

Crossrefs

Cf. A000265, A080224, A187795.

Subsequence of A005101.

Subsequences: A006038, A381547.

Programs

Mathematica

q[n_] := OddQ[DivisorSum[n, # &, DivisorSigma[-1, #] > 2 &]]; Select[Range[13000], q]

PARI

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