A381547 -id:A381547 - cp's OEIS frontend

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

Amiram Eldar, Feb 26 2025

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.

			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.

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

Cf. A080224.
Subsequence of A005101.
Subsequences: A091191, A381547, A381548, A381549.

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

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

A381550 Numbers whose sum of abundant divisors is odd.

Original entry on oeis.org

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

Amiram Eldar, Feb 26 2025

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.

			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.

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

Cf. A000265, A080224, A187795.
Subsequence of A005101.
Subsequences: A006038, A381547.

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

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

cp's OEIS Frontend

A381546 Numbers with an odd number of abundant divisors.

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