cp's OEIS Frontend

A357460 Numbers whose number of deficient divisors is equal to their number of nondeficient divisors.

%I A357460 #12 Sep 30 2022 04:25:21
%S A357460 72,108,120,168,180,252,420,528,560,624,1188,1224,1368,1400,1404,1632,
%T A357460 1656,1824,1836,1960,1980,2040,2052,2088,2208,2232,2280,2340,2484,
%U A357460 2664,2760,2772,2784,2856,2952,2976,3060,3096,3132,3192,3200,3276,3348,3384,3420,3432
%N A357460 Numbers whose number of deficient divisors is equal to their number of nondeficient divisors.
%C A357460 Numbers k such that A080226(k) = A341620(k).
%C A357460 This sequence is infinite: if p >= 17 is a prime then 72*p is a term.
%C A357460 The least odd term of this sequence is a(36126824) = A357461(1) = 3010132125.
%C A357460 Since the number of divisors of any term is even, none of the terms are squares.
%C A357460 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 A357460 Amiram Eldar, <a href="/A357460/b357460.txt">Table of n, a(n) for n = 1..10000</a>
%e A357460 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 A357460 q[n_] := DivisorSum[n, If[DivisorSigma[-1, #] < 2, 1, -1] &] == 0; Select[Range[3500], q]
%o A357460 (PARI) is(n) = sumdiv(n, d, if(sigma(d, -1) < 2, 1, -1)) == 0;
%Y A357460 Subsequence of A000037 and A005101.
%Y A357460 Cf. A080226, A335543, A335544, A341620, A357461, A357462.
%K A357460 nonn
%O A357460 1,1
%A A357460 _Amiram Eldar_, Sep 29 2022