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 A346551 3-Sondow numbers: numbers k such that p^s divides k/p + 3 for every prime power divisor p^s of k. 8
 1, 2, 10, 18, 126, 5418, 141174, 6643507266, 157486189806 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers k such that A235137(k) == 3 (mod k). A positive integer k is a 3-Sondow number if satisfies any of the following equivalent properties: 1) p^s divides k/p + 3 for every prime power divisor p^s of k. 2) 3/k + Sum_{prime p|k} 1/p is an integer. 3) 3 + Sum_{prime p|k} k/p == 0 (mod k). 4) Sum_{i=1..k} i^phi(k) == 3 (mod k). LINKS Github, Jonathan Sondow (1943 - 2020) J. M. Grau, A. M. Oller-Marcén, and D. Sadornil, On µ-Sondow Numbers, arXiv:2111.14211 [math.NT], 2021. J. M. Grau, A. M. Oller-Marcen  and J. Sondow, On the congruence 1^n + 2^n +... + n^n = d (mod n), where d divides n, arXiv:1309.7941 [math.NT], 2013-2014. MATHEMATICA Sondow[mu_][n_]:= Sondow[mu][n]= Module[{fa=FactorInteger[n]}, IntegerQ[mu/n+Sum[1/fa[[i, 1]], {i, Length[fa]}]]] Select[Range[1000000], Sondow[3][#]&] CROSSREFS Cf. A054377, A007850, A235137, A348058, A348059. (-1) and (-2) -Sondow numbers: A326715, A330069. 1-Sondow to 9-Sondow numbers: A349193, A330068, A346551, A346552, A346553, A346554, A346555, A346556, A346557. Sequence in context: A317714 A055260 A254059 * A180591 A330083 A322951 Adjacent sequences: A346548 A346549 A346550 * A346552 A346553 A346554 KEYWORD nonn,more AUTHOR José María Grau Ribas, Dec 04 2021 EXTENSIONS a(8)-a(9) from Martin Ehrenstein, Dec 31 2021 STATUS approved

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Last modified February 7 08:55 EST 2023. Contains 360115 sequences. (Running on oeis4.)