A362268 - OEIS

%I #7 Apr 14 2023 02:11:37

%S 20,60,180,189,400,540,1200,1372,1620,2541,2835,3185,3600,4860,5577,

%T 6860,8000,10800,14365,14580,16093,23465,24000,28812,32400,34300,

%U 34375,35721,40733,42525,43740,46529,72000,78793,97200,123101,131220,135401,139755,144060

%N Numbers whose prime factors counted with multiplicity satisfy: (maximum) - (minimum) = (mean).

%e The terms together with their prime factors begin:

%e     20: [2, 2, 5]

%e     60: [2, 2, 3, 5]

%e    180: [2, 2, 3, 3, 5]

%e    189: [3, 3, 3, 7]

%e    400: [2, 2, 2, 2, 5, 5]

%e    540: [2, 2, 3, 3, 3, 5]

%e   1200: [2, 2, 2, 2, 3, 5, 5]

%e   1372: [2, 2, 7, 7, 7]

%e   1620: [2, 2, 3, 3, 3, 3, 5]

%e   2541: [3, 7, 11, 11]

%e   2835: [3, 3, 3, 3, 5, 7]

%e   3185: [5, 7, 7, 13]

%e   3600: [2, 2, 2, 2, 3, 3, 5, 5]

%e   4860: [2, 2, 3, 3, 3, 3, 3, 5]

%e The prime factors of 4860 are [2, 2, 3, 3, 3, 3, 3, 5], with minimum 2, maximum 5, and mean 3, and 5-2 = 3, so 4860 is in the sequence.

%o (Python)

%o from itertools import count, islice

%o from math import prod

%o from sympy import factorint

%o def A362268_gen(startvalue=2): # generator of terms >= startvalue

%o     return filter(lambda n:(max(f:=factorint(n))-min(f))*sum(f.values())==sum(map(prod,f.items())),count(max(startvalue,2)))

%o A362268_list = list(islice(A362268_gen(),20))

%Y Cf. A362047.

%K nonn

%O 1,1

%A _Chai Wah Wu_, Apr 13 2023