cp's OEIS Frontend

A381547 Odd numbers with an odd number of abundant divisors.

%I A381547 #7 Feb 27 2025 06:42:46
%S A381547 945,1575,2205,3465,4095,4725,5355,5775,5985,6435,6615,6825,7245,7425,
%T A381547 8085,8415,8505,8925,9135,9555,9765,10395,11025,11655,12285,12705,
%U A381547 12915,13545,14175,14805,15015,16065,16695,17955,18585,19215,19635,19845,21105,21735,21945
%N A381547 Odd numbers with an odd number of abundant divisors.
%C A381547 Odd numbers k such that A080224(k) is odd.
%C A381547 Also, odd numbers with an odd sum of abundant divisors.
%C A381547 The odd primitive abundant numbers (A006038) are all terms of this sequence since A080224(A006038(n)) = 1 for all n.
%H A381547 Amiram Eldar, <a href="/A381547/b381547.txt">Table of n, a(n) for n = 1..10000</a>
%e A381547 945 is a term since it is odd, and it has only one abundant divisor, 945 itself.
%e A381547 4725 is a term since it is odd, and it has 3 abundant divisors, 945, 1575 and 4725.
%e A381547 14175 is a term since it is odd, and it has 5 abundant divisors, 945, 1575, 2835, 4725 and 14175.
%t A381547 q[n_] := OddQ[DivisorSum[n, 1 &, DivisorSigma[-1, #] > 2 &]]; Select[Range[1, 22000, 2], q]
%o A381547 (PARI) isok(k) = if(k % 2, sumdiv(k, d, (sigma(d, -1) > 2)) % 2, 0);
%Y A381547 Cf. A080224, A187795.
%Y A381547 Intersection of A005408 and A381546.
%Y A381547 Subsequence of A005231.
%Y A381547 Subsequences: A006038, A381548, A381549.
%K A381547 nonn,easy
%O A381547 1,1
%A A381547 _Amiram Eldar_, Feb 26 2025