

A256533


Product of n and the sum of all divisors of all positive integers <= n.


4



1, 8, 24, 60, 105, 198, 287, 448, 621, 870, 1089, 1524, 1833, 2310, 2835, 3520, 4046, 4986, 5643, 6780, 7791, 8954, 9913, 11784, 13050, 14664, 16308, 18480, 20010, 22860, 24614, 27424, 29865, 32606, 35245, 39528, 42032, 45448, 48828, 53680, 56744, 62160, 65532, 70752, 75870, 80868, 84882, 92640, 97363, 104000
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OFFSET

1,2


COMMENTS

a(n) is also sum of the volumes (or the total number of unit cubes) from two complementary polycubes: the irregular staircase after nth stage described in A244580, and the irregular step pyramid after (n1)st stage described in A245092. Note that in both structures the horizontal area in the nth level is also the symmetric representation of sigma(n). This comment is represented by the third formula.


LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = n*A024916(n) = n^3  A256532(n).
a(n) = A143128(n) + A175254(n1), n > 1.


EXAMPLE

For n = 3; a(3) = 3 * 8 = 19 + 5 = 24.


MATHEMATICA

a[n_]:=n*Apply[Plus, Flatten[Divisors[Range[n]]]]; Array[a, 50] (* Ivan N. Ianakiev, May 03 2015 *)


PROG

(Python)
def A256533(n):
....s=0
....for k in range(1, n+1):
........s+=n%k
....return (n**3)(s*n) # Indranil Ghosh, Feb 13 2017


CROSSREFS

Cf. A000203, A000578, A024916, A064987, A143128, A175254, A196020, A236104, A237270, A237271, A237593, A244580, A245092, A245100, A256532.
Sequence in context: A099041 A306056 A129959 * A177719 A317234 A049724
Adjacent sequences: A256530 A256531 A256532 * A256534 A256535 A256536


KEYWORD

nonn


AUTHOR

Omar E. Pol, May 02 2015


STATUS

approved



