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A335543 Numbers with an equal number of deficient and abundant divisors. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A217584 A030633 A189988

Adjacent sequences:  A335540 A335541 A335542 * A335544 A335545 A335546

KEYWORD

nonn

AUTHOR

Amiram Eldar, Jun 13 2020

STATUS

approved

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Last modified June 15 22:06 EDT 2021. Contains 345053 sequences. (Running on oeis4.)