%I #12 Sep 30 2022 04:25:21

%S 72,108,120,168,180,252,420,528,560,624,1188,1224,1368,1400,1404,1632,

%T 1656,1824,1836,1960,1980,2040,2052,2088,2208,2232,2280,2340,2484,

%U 2664,2760,2772,2784,2856,2952,2976,3060,3096,3132,3192,3200,3276,3348,3384,3420,3432

%N Numbers whose number of deficient divisors is equal to their number of nondeficient divisors.

%C Numbers k such that A080226(k) = A341620(k).

%C This sequence is infinite: if p >= 17 is a prime then 72*p is a term.

%C The least odd term of this sequence is a(36126824) = A357461(1) = 3010132125.

%C Since the number of divisors of any term is even, none of the terms are squares.

%C The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 1, 10, 131, 1172, 12003, 120647, 1199147, 11992293, 120089446, ... . Apparently, the asymptotic density of this sequence exists and is equal to about 0.012.

%H Amiram Eldar, <a href="/A357460/b357460.txt">Table of n, a(n) for n = 1..10000</a>

%e 72 is a term since it has 12 divisors, 6 of them (1, 2, 3, 4, 8 and 9) are deficient and 6 (6, 12, 18, 24, 36 and 72) are not.

%t q[n_] := DivisorSum[n, If[DivisorSigma[-1, #] < 2, 1, -1] &] == 0; Select[Range[3500], q]

%o (PARI) is(n) = sumdiv(n, d, if(sigma(d, -1) < 2, 1, -1)) == 0;

%Y Subsequence of A000037 and A005101.

%Y Cf. A080226, A335543, A335544, A341620, A357461, A357462.

%K nonn

%O 1,1

%A _Amiram Eldar_, Sep 29 2022