login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A119616 Second elementary symmetric function of divisors of n. 5
0, 2, 3, 14, 5, 47, 7, 70, 39, 97, 11, 287, 13, 163, 158, 310, 17, 533, 19, 609, 262, 343, 23, 1375, 155, 457, 390, 1043, 29, 1942, 31, 1302, 542, 733, 502, 3185, 37, 895, 718, 2945, 41, 3358, 43, 2247, 1859, 1267, 47, 5983, 399, 2697, 1142, 3017, 53, 5150, 1006 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(p)=p if p is prime and records are A002093 (highly abundant numbers). - Robert G. Wilson v, Jun 07 2006

LINKS

T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

FORMULA

a(n) = Sum_{u|n, v|n, u<v} u*v.

a(n) = (sigma_1(n)^2-sigma_2(n))/2, cf. A000203, A001157. - Vladeta Jovovic, Jun 07 2006

EXAMPLE

|-------+------------------------------------------+---------------------|

|...n...|................divisors(n)...............|..s2(divisors.(n))...|

|-------+------------------------------------------+---------------------|

|...1...|....................1.....................|..........0..........|

|...2...|...................1,2....................|..........2..........|

|...3...|...................1,3....................|..........3..........|

|...4...|..................1,2,4...................|.........14..........|

|...5...|...................1,5....................|..........5..........|

|...6...|.................1,2,3,6..................|.........47..........|

MAPLE

a:= n-> (l-> add(add(l[i]*l[j], i=1..j-1), j=2..nops(l)))

        (sort([numtheory[divisors](n)[]])):

seq(a(n), n=1..80);  # Alois P. Heinz, Jun 25 2014

MATHEMATICA

f[n_] := Block[{d = Divisors@n}, Sum[ d[[u]]*d[[v]], {v, 2, Length@d}, {u, v - 1}]]; Array[f, 55] (* Robert G. Wilson v *)

PROG

(PARI) a(n)=my(d=divisors(n)); sum(i=1, #d-1, sum(j=i+1, #d, d[i]*d[j])) \\ Charles R Greathouse IV, Mar 05 2013

(PARI) a(n)=(sigma(n)^2-sigma(n, 2))/2 \\ Charles R Greathouse IV, Mar 05 2013

CROSSREFS

Cf. A002093, A000203, A001157, A067692.

Column k=2 of A224381.

Sequence in context: A321226 A337329 A329365 * A286968 A285818 A287759

Adjacent sequences:  A119613 A119614 A119615 * A119617 A119618 A119619

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, based on email from Neven Juric (neven.juric(AT)apis-it.hr), Jun 07 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 12 01:36 EDT 2021. Contains 342912 sequences. (Running on oeis4.)