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 A309272 Numbers m such that m divides A173290(m) = Sum_{k=1..m} psi(k), where psi is the Dedekind psi function (A001615). 0
 1, 2, 5, 15, 31, 40, 66, 81, 315, 966, 1398, 1768, 30166, 32335, 98734, 388033, 591597, 1375056, 14966304, 15160528, 50793208, 51302236, 99253376, 110994356, 230465053, 402340268, 497982399, 2027319577, 2879855394, 18450762682, 29922126368, 31711273834, 40583934786 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The corresponding quotients are 1, 2, 4, 12, 24, 31, 51, 62, 240, 735, 1063, 1344, 22924, 24572, 75029, 294870, 449560, 1044918, 11373028, 11520620, 38598210, 38985025, 75423522, 84345597, 175132440, 305741942, 378421246, 1540578144, 2188427680, 14020898356, 22738089456, 24097678498, 30840092321, ... LINKS Table of n, a(n) for n=1..33. EXAMPLE 2 is in the sequence since psi(1) + psi(2) = 1 + 3 = 4 is divisible by 2. 5 is in the sequence since psi(1) + psi(2) + ... + psi(5) = 1 + 3 + 4 + 6 + 6 = 20 is divisible by 5. MATHEMATICA psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); seq = {}; s = 0; Do[s += psi[n]; If[Divisible[s, n], AppendTo[seq, n]], {n, 1, 10^4}]; seq CROSSREFS Cf. A001615, A173290. Cf. A045345, A048290, A050226, A056550, A063971, A064605, A064606, A064607, A064610, A064611, A064612, A306950, A307043, A307161, A326488. Sequence in context: A290836 A191313 A078528 * A077686 A034499 A299159 Adjacent sequences: A309269 A309270 A309271 * A309273 A309274 A309275 KEYWORD nonn AUTHOR Amiram Eldar, Oct 23 2019 EXTENSIONS a(31)-a(33) from Giovanni Resta, Oct 24 2019 STATUS approved

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Last modified October 3 16:28 EDT 2023. Contains 365868 sequences. (Running on oeis4.)