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 A220847 a(n) = numerator of the fraction whose Engel expansion has the positive divisors of n as its terms. 1
 1, 3, 4, 13, 6, 61, 8, 105, 37, 161, 12, 2965, 14, 309, 316, 1681, 18, 9901, 20, 13221, 610, 749, 24, 569401, 151, 1041, 1000, 36093, 30, 1381981, 32, 53793, 1486, 1769, 1506, 17294509, 38, 2205, 2068, 4232841, 42, 5285869, 44, 139437, 128296, 3221, 48 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: sequence is injective (all terms of this sequence occur only once). LINKS Jaroslav Krizek, Table of n, a(n) for n = 1..100 FORMULA a(n) = sum_(d|n) (product_(d|n) d) / (product_( d_x|n , d_x<=d) d_x) = sum_(d|n) (A007955(n)) / (product_( d_x|n , d_x<=d) d_x). a(p) = p + 1 for prime p. EXAMPLE The divisors of 6 are 1, 2, 3, 6. So a(6) is the numerator of 1/1+1/(1*2)+1/(1*2*3)+1/(1*2*3*6)=61/36. a(6) = 36/1+36/(1*2)+36/(1*2*3)+36/(1*2*3*6)=36+18+6+1=61. CROSSREFS Cf. A007955 (denominators). Sequence in context: A242648 A327583 A324159 * A127611 A308688 A324501 Adjacent sequences: A220844 A220845 A220846 * A220848 A220849 A220850 KEYWORD nonn AUTHOR Jaroslav Krizek, Dec 22 2012 STATUS approved

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Last modified June 2 16:59 EDT 2023. Contains 363099 sequences. (Running on oeis4.)