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A365398
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Length of the longest subsequence of 1, ..., n on which sigma, the sum of the divisors of n (A000203), is nondecreasing.
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12
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1, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 21, 21, 21, 21, 22, 22, 22, 23, 24, 24, 25, 25, 25
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OFFSET
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1,2
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COMMENTS
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The sequence was inspired by A365339. In particular, note remark (4.4) by Terence Tao in the linked paper.
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LINKS
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FORMULA
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a(n+1) - a(n) <= 1.
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PROG
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(Python)
from bisect import bisect
from sympy import divisor_sigma
plist, qlist, c = tuple(divisor_sigma(i) for i in range(1, n+1)), [0]*(n+1), 0
for i in range(n):
qlist[a:=bisect(qlist, plist[i], lo=1, hi=c+1, key=lambda x:plist[x])]=i
c = max(c, a)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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