A361206 Lexicographically earliest infinite sequence of distinct imperfect numbers such that the sum of the abundance of all terms is never < 1.
12, 1, 2, 4, 18, 3, 8, 20, 10, 24, 5, 7, 16, 30, 9, 14, 32, 36, 11, 13, 40, 15, 42, 17, 48, 19, 21, 54, 22, 44, 56, 50, 60, 23, 25, 52, 64, 66, 26, 70, 72, 27, 29, 34, 78, 45, 80, 33, 68, 84, 31, 35, 88, 90, 37, 38, 96, 39, 41, 100, 46, 102, 76, 104, 108, 43, 58
Offset: 1
Examples
The sequence starts with a(1) = 12, since 12 is the first imperfect number with abundance greater than 0. Then the next term not yet in the sequence, such that s is not less than 1, is 1. a(5) is the next abundant number 18, since any deficient number would bring s below 1. n : 1 2 3 4 5 6 7 8 9 10 a(n): 12 1 2 4 18 3 8 20 10 24 s : 4 3 2 1 4 2 1 3 1 13
Programs
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Python
from sympy.ntheory import abundance from itertools import count, filterfalse def A361206_list(nmax): A,s = [],0 for n in range(1,nmax+1): A2 = set(A) for y in filterfalse(A2._contains_,count(1)): ab = abundance(y) if ab != 0 and ab + s >= 1: A.append(y) s += ab break return(A)
Comments