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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):

.                 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

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.                |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|

.

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.)