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 A286873 Numbers x such that x = Sum_{i=1..k} (x mod d_(x-i)) + Sum_{i=1..k} (x mod d_(x+i)) for some k, where d_(x-i) and d_(x+i) are the aliquot parts of (x-i) and (x+i). 2
 7, 10, 16, 27, 75, 87, 109, 120, 151, 1887, 4029, 5829, 17815, 39780, 62485, 238021, 254011, 437744, 779391, 873565, 979389, 1713591, 2409697, 4194303, 4199029, 4607295, 8353791, 9928791, 15370303, 21381096, 33653887, 114203775, 124540389, 2146926591, 6521655540 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Values of k for the listed terms are 2, 2, 2, 2, 2, 1, 1, 3, 1, 1, 1, 1, 1, 3, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, ... If d_(x-i) were the aliquot parts of (x-i) and d_(x+i) the divisors of (x+i) we would get the average of twin prime pairs (A014574). If d_(x-i) were the divisors of (x-i) and d_(x+i) the aliquot parts of (x+i) we would get 5, 6, 7, 1296, 3228, 32767, 65784, 128766, 711236, ... LINKS EXAMPLE For 7 the value of k is 2. Aliquot parts of 5, 6, 8 and 9 are: [1], [1, 2, 3], [1, 2, 4], [1, 3]. Residues are 0 + 0 + 1 + 1 + 0 + 1 + 3 + 0 + 1 that sum up to 7. MAPLE with(numtheory): P:=proc(q) local a, b, c, j, k, n; for n from 3 to q do a:=0; k:=0; while a

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Last modified June 4 08:18 EDT 2020. Contains 334825 sequences. (Running on oeis4.)