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

1,1

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.

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000265, A080224, A187795.

Subsequence of A005101.

Subsequences: A006038, A381547.

Sequence in context: A294576 A252192 A252185 * A005231 A174865 A174535

Adjacent sequences: A381547 A381548 A381549 * A381551 A381552 A381553

Keyword

nonn,easy

Author

Amiram Eldar, Feb 26 2025

Status

approved