

A330866


a(n) = Sum_{dn, d<n} (n/d) * (nd).


0



0, 2, 6, 16, 20, 48, 42, 88, 90, 140, 110, 264, 156, 280, 300, 416, 272, 594, 342, 720, 588, 704, 506, 1248, 700, 988, 972, 1400, 812, 1920, 930, 1824, 1452, 1700, 1540, 2952, 1332, 2128, 2028, 3280, 1640, 3696, 1806, 3432, 3240, 3128, 2162, 5472, 2646, 4350, 3468
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..51.


FORMULA

a(p^k) = p^k * (p^(k+1)  p*(k+1) + k) / (p1), where p is prime and k is a positive integer.


EXAMPLE

a(6) = 48; The proper divisors of 6 are 1, 2 and 3. We have (6/1)*(61) + (6/2)*(62) + (6/3)*(63) = 30 + 12 + 6 = 48.


MATHEMATICA

Table[Sum[(n/i) (ni) (1  Ceiling[n/i] + Floor[n/i]), {i, n1}], {n, 80}]


PROG

(PARI) a(n)={sumdiv(n, d, (nd)*n/d)} \\ Andrew Howroyd, Apr 28 2020


CROSSREFS

Cf. A001065.
Sequence in context: A082374 A085226 A260376 * A071522 A192532 A230853
Adjacent sequences: A330863 A330864 A330865 * A330867 A330868 A330869


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Apr 28 2020


STATUS

approved



