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Search: id:A119616
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| A119616 |
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Second elementary symmetric function of divisors of n. |
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+0
2
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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a(p)=p if p is prime and records are A002093: Highly abundant numbers. - Robert G. Wilson v Jun 07 2006.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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Sum_{u|n, v|n, u<v} u*v.
a(n) = (sigma_1(n)^2-sigma_2(n))/2, cf. A000203, A001157. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 07 2006
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EXAMPLE
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|-------+------------------------------------------+---------------------|
|...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..........|
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A067692.
Sequence in context: A094003 A093553 A027673 this_sequence A056435 A032806 A041009
Adjacent sequences: A119613 A119614 A119615 this_sequence A119617 A119618 A119619
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), based on email from Neven Juric (neven.juric(AT)apis-it.hr), Jun 07 2006
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