

A060872


Sum of d*d' over all unordered pairs (d,d') with d*d' = n.


4



1, 2, 3, 8, 5, 12, 7, 16, 18, 20, 11, 36, 13, 28, 30, 48, 17, 54, 19, 60, 42, 44, 23, 96, 50, 52, 54, 84, 29, 120, 31, 96, 66, 68, 70, 180, 37, 76, 78, 160, 41, 168, 43, 132, 135, 92, 47, 240, 98, 150, 102, 156, 53, 216, 110, 224, 114, 116, 59, 360, 61, 124, 189, 256
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OFFSET

1,2


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..5000


FORMULA

a(n) = n * ceiling( d(n)/2) where d is the number of divisors function.
G.f.: x*f'(x), where f(x) = Sum_{k>=1} x^k^2/(1  x^k).  Ilya Gutkovskiy, Apr 10 2017


EXAMPLE

a(4)=8 because pairs of factors are 1*4 and 2*2 and 1*4 + 2*2 = 8.


MATHEMATICA

Table[ n * Ceiling[ DivisorSigma[0, n] /2 ], {n, 1, 73} ]


PROG

(MAGMA) [n*Ceiling(DivisorSigma(0, n)/2): n in [1..70]]; // Vincenzo Librandi, Apr 12 2017


CROSSREFS

Cf. A060866.
First differences of A083356.
Sequence in context: A011433 A126139 A296070 * A162775 A066959 A086471
Adjacent sequences: A060869 A060870 A060871 * A060873 A060874 A060875


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, May 04 2001


EXTENSIONS

More terms from Robert G. Wilson v, Jun 23 2001


STATUS

approved



