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erdős #49

← #48 · #50 → (packet.json; erdosproblems.com)

Let $A = {a_{1} < \dots < a_{t}} \subseteq {1, \dots, N}$ be such that $ϕ (a_{1}) < \dots < ϕ (a_{t})$ . The primes are such an example. Are they the largest possible? Can one show that $∣ A ∣ < (1 + o (1)) π (N)$ or even $∣ A ∣ = o (N)$ ?

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number theory · solved · 0 attempts

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A365339 — Length of the longest subsequence of 1,...,n on which the Euler totient function phi A000010 is nondecreasing.1,2,3,4,5,5,6,6,7,7,8,8,9,9,10,11,12,12,13,13,13,13,14,14,14,14,15,15,16,16,17,17,17,17,18,18,19,19,19,19,20,20,21,21,21 A365474 — a(n) = A365339(10^n).1,7,34,193,1276,9656,78562,664643,5761519,50847598

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finding.noted · reviewer:will-blair · 1 day

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