A363170 -id:A363170 - cp's OEIS frontend

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

Amiram Eldar, May 19 2023

nonn

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.

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

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

Intersection of A001694 and A005101.
Cf. A180114, A363170, A363171.
Subsequences: A307959, A328136, A356871.

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

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

cp's OEIS Frontend

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

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