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

1,1

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.

Links

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

Formula

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

Example

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}.

Mathematica

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

Crossrefs

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

Sequence in context: A125841 A320457 A154051 * A366854 A217584 A030633

Adjacent sequences: A335540 A335541 A335542 * A335544 A335545 A335546

Keyword

nonn

Author

Amiram Eldar, Jun 13 2020

Status

approved