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 A365737 Length of the longest subsequence of 1,...,n on which the Euler totient function phi A000010 is nonincreasing. 7
 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 Paul Pollack, Carl Pomerance and Enrique Treviño, Sets of monotonicity for Euler's totient function, preprint. See M↓(n). Paul Pollack, Carl Pomerance and Enrique Treviño, Sets of monotonicity for Euler's totient function, Ramanujan J. 30 (2013), no. 3, 379--398. Terence Tao, Monotone non-decreasing sequences of the Euler totient function, arXiv:2309.02325 [math.NT], 2023. PROG (Python) from bisect import bisect from sympy import totient def A365737(n): plist, qlist, c = tuple(-totient(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) return c CROSSREFS Cf. A000010, A000720. Cf. A365339, A365398, A365399, A365400, A365474, A061070. Sequence in context: A242768 A365742 A064557 * A023967 A278163 A347635 Adjacent sequences: A365734 A365735 A365736 * A365738 A365739 A365740 KEYWORD nonn AUTHOR Chai Wah Wu, Sep 17 2023 STATUS approved

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Last modified July 25 09:25 EDT 2024. Contains 374587 sequences. (Running on oeis4.)