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A363169
Powerful abundant numbers: numbers that are both powerful (A001694) and abundant (A005101).
6
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.
Subsequences: A307959, A328136, A356871.
Sequence in context: A286708 A355462 A363216 * A114127 A322658 A224830
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 19 2023
STATUS
approved