A335543 Numbers with an equal number of deficient and abundant divisors.

144, 324, 336, 756, 900, 1176, 1848, 2100, 2184, 2940, 3200, 3520, 4000, 4160, 4400, 5200, 5952, 10880, 11440, 12160, 12348, 12544, 13600, 14720, 15200, 16368, 17360, 18304, 18400, 18560, 19344, 19360, 19404, 22932, 23200, 27040, 28600, 29988, 33516, 40572, 47124

Offset: 1

Author

Amiram Eldar, Jun 13 2020

Keywords

• nonn

Comments

This sequence is infinite. For example, 3200*p is a term for all primes p >= 257.

The least odd term of this sequence is a(1273824) = 3010132125.

Examples

			144 is a term since it has 7 deficient divisors: {1, 2, 3, 4, 8, 9, 16} and 7 abundant divisors: {12, 18, 24, 36, 48, 72, 144}.
		

Links

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

Crossrefs

Cf. A000203, A005100, A005101, A080224, A080226, A335544.

Programs

Mathematica

ab[n_] := DivisorSigma[1, n] - 2n; eqdivQ[n_] := Count[(abs = ab/@Divisors[n]), ?(# > 0 &)] == Count[abs, ?(# < 0 &)]; Select[Range[50000], eqdivQ]

Formula

Numbers k such that A080224(k) = A080226(k).