A363169 Powerful abundant numbers: numbers that are both powerful (A001694) and abundant (A005101).

36, 72, 100, 108, 144, 196, 200, 216, 288, 324, 392, 400, 432, 500, 576, 648, 784, 800, 864, 900, 968, 972, 1000, 1152, 1296, 1352, 1372, 1568, 1600, 1728, 1764, 1800, 1936, 1944, 2000, 2304, 2500, 2592, 2700, 2704, 2744, 2916, 3136, 3200, 3456, 3528, 3600, 3872, 3888, 4000

Offset

1,1

Comments

The least odd term is a(90) = 11025, and the least term that is coprime to 6 is 1382511906801025.

Are there two consecutive integers in this sequence? There are none below 10^22.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10534 (terms not exceeding 10^8)

Example

36 = 2^2 * 3^2 is a term since it is powerful, and sigma(36) = 91 > 2*36 = 72.

Mathematica

Select[Range[4000], DivisorSigma[-1, #] > 2 && Min[FactorInteger[#][[;; , 2]]] > 1 &]

Prog

(PARI) is(n) = { my(f = factor(n)); n > 1 && vecmin(f[, 2]) > 1 && sigma(f, -1) > 2; }

Crossrefs

Intersection of A001694 and A005101.

Cf. A180114, A363170, A363171.

Subsequences: A307959, A328136, A356871.

Sequence in context: A286708 A355462 A363216 * A114127 A322658 A224830

Adjacent sequences: A363166 A363167 A363168 * A363170 A363171 A363172

Keyword

nonn

Author

Amiram Eldar, May 19 2023

Status

approved