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A381550
Numbers whose sum of abundant divisors is odd.
1
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
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
Subsequence of A005101.
Subsequences: A006038, A381547.
Sequence in context: A294576 A252192 A252185 * A005231 A174865 A174535
KEYWORD
nonn,easy,new
AUTHOR
Amiram Eldar, Feb 26 2025
STATUS
approved