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A346551
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3-Sondow numbers: numbers k such that p^s divides k/p + 3 for every prime power divisor p^s of k.
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8
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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J. M. Grau, A. M. Oller-Marcén, and D. Sadornil, On µ-Sondow Numbers, arXiv:2111.14211 [math.NT], 2021.
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MATHEMATICA
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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][#]&]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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