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 A243980 Four times the sum of all divisors of all positive integers <= n. 8
 4, 16, 32, 60, 84, 132, 164, 224, 276, 348, 396, 508, 564, 660, 756, 880, 952, 1108, 1188, 1356, 1484, 1628, 1724, 1964, 2088, 2256, 2416, 2640, 2760, 3048, 3176, 3428, 3620, 3836, 4028, 4392, 4544, 4784, 5008, 5368, 5536, 5920, 6096, 6432, 6744, 7032, 7224, 7720 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also partial sums of A239050. Also number of "ON" cells at n-th stage in a structure which looks like a simple 2-dimensional cellular automaton (see example). The structure is formed by the reflection on the four quadrants from the diagram of the symmetry of sigma in the first quadrant after n-th stage, hence the area in each quadrant equals the area of each wedge and equals A024916(n); the sum of all divisors of all positive integers <= n. For more information about the diagram see A237593 and A237270. LINKS Indranil Ghosh, Table of n, a(n) for n = 1..7342 FORMULA a(n) = A016742(n) - 4*A004125(n) = 4*A024916(n) EXAMPLE Illustration of the structure after 16 stages (contains 880 ON cells): .                 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .                |  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  | .                | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | .             _ _| |  _ _ _ _ _ _ _ _ _ _ _ _ _ _  | |_ _ .           _|  _ _| |_ _ _ _ _ _ _ _ _ _ _ _ _ _| |_ _  |_ .         _|  _|  _| |  _ _ _ _ _ _ _ _ _ _ _ _  | |_  |_  |_ .        |  _|   |_ _| |_ _ _ _ _ _ _ _ _ _ _ _| |_ _|   |_  | .   _ _ _| |  _ _|     |  _ _ _ _ _ _ _ _ _ _  |     |_ _  | |_ _ _ .  |  _ _ _|_| |      _| |_ _ _ _ _ _ _ _ _ _| |_      | |_|_ _ _  | .  | | |  _ _ _|    _|_ _|  _ _ _ _ _ _ _ _  |_ _|_    |_ _ _  | | | .  | | | | |  _ _ _| |  _| |_ _ _ _ _ _ _ _| |_  | |_ _ _  | | | | | .  | | | | | | |  _ _|_|  _|  _ _ _ _ _ _  |_  |_|_ _  | | | | | | | .  | | | | | | | | |  _ _|   |_ _ _ _ _ _|   |_ _  | | | | | | | | | .  | | | | | | | | | | |  _ _|  _ _ _ _  |_ _  | | | | | | | | | | | .  | | | | | | | | | | | | |  _|_ _ _ _|_  | | | | | | | | | | | | | .  | | | | | | | | | | | | | | |  _ _  | | | | | | | | | | | | | | | .  | | | | | | | | | | | | | | | |   | | | | | | | | | | | | | | | | .  | | | | | | | | | | | | | | | |_ _| | | | | | | | | | | | | | | | .  | | | | | | | | | | | | | |_|_ _ _ _|_| | | | | | | | | | | | | | .  | | | | | | | | | | | |_|_  |_ _ _ _|  _|_| | | | | | | | | | | | .  | | | | | | | | | |_|_    |_ _ _ _ _ _|    _|_| | | | | | | | | | .  | | | | | | | |_|_ _  |_  |_ _ _ _ _ _|  _|  _ _|_| | | | | | | | .  | | | | | |_|_ _  | |_  |_ _ _ _ _ _ _ _|  _| |  _ _|_| | | | | | .  | | | |_|_ _    |_|_ _| |_ _ _ _ _ _ _ _| |_ _|_|    _ _|_| | | | .  | |_|_ _ _  |     |_  |_ _ _ _ _ _ _ _ _ _|  _|     |  _ _ _|_| | .  |_ _ _  | |_|_      | |_ _ _ _ _ _ _ _ _ _| |      _|_| |  _ _ _| .        | |_    |_ _  |_ _ _ _ _ _ _ _ _ _ _ _|  _ _|    _| | .        |_  |_  |_  | |_ _ _ _ _ _ _ _ _ _ _ _| |  _|  _|  _| .          |_  |_ _| |_ _ _ _ _ _ _ _ _ _ _ _ _ _| |_ _|  _| .            |_ _  | |_ _ _ _ _ _ _ _ _ _ _ _ _ _| |  _ _| .                | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | .                | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | .                |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| . MATHEMATICA Accumulate[4*DivisorSigma[1, Range[50]]] (* Harvey P. Dale, May 13 2018 *) CROSSREFS Cf. A000203, A000290, A004125, A016742, A024916, A175254, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239050, A239660, A239931-A239934, A244050. Sequence in context: A046001 A239611 A031050 * A119677 A326873 A126032 Adjacent sequences:  A243977 A243978 A243979 * A243981 A243982 A243983 KEYWORD nonn AUTHOR Omar E. Pol, Jun 18 2014 STATUS approved

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Last modified September 16 18:24 EDT 2019. Contains 327116 sequences. (Running on oeis4.)