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A000441 Sum(k*sigma(k)*sigma(n-k),k=1..n-1).
(Formerly M4613 N1968)
4
0, 1, 9, 34, 95, 210, 406, 740, 1161, 1920, 2695, 4116, 5369, 7868, 9690, 13640, 16116, 22419, 25365, 34160, 38640, 50622, 55154, 73320, 77225, 100100, 107730, 135576, 141085, 182340, 184760, 233616, 243408, 297738, 301420, 385110, 377511, 467210, 478842 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

J. Touchard, On prime numbers and perfect numbers, Scripta Math., 129 (1953), 35-39.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..1000

J. Touchard, On prime numbers and perfect numbers, Scripta Math., 129 (1953), 35-39. [Annotated scanned copy]

FORMULA

a(n) = sum(k=1..n-1, k * sigma(k) * sigma(n-k) ). Convolution of A000203 with A064987. - Sean A. Irvine, Nov 14 2010

MAPLE

S:=(n, e)->add(k^e*sigma(k)*sigma(n-k), k=1..n-1);

f:=e->[seq(S(n, e), n=1..30)]; f(1); # from N. J. A. Sloane, Jul 03 2015

MATHEMATICA

a[n_] := Sum[k*DivisorSigma[1, k]*DivisorSigma[1, n-k], {k, 1, n-1}]; Array[a, 40] (* Jean-Fran├žois Alcover, Feb 08 2016 *)

PROG

(PARI) a(n) = sum(k=1, n-1, k*sigma(k)*sigma(n-k)); \\ Michel Marcus, Feb 02 2014

CROSSREFS

Cf. A000441, A000499.

Sequence in context: A279128 A014816 A147691 * A067989 A002881 A268803

Adjacent sequences:  A000438 A000439 A000440 * A000442 A000443 A000444

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Sean A. Irvine, Nov 14 2010

a(1)=0 prepended by Michel Marcus, Feb 02 2014

STATUS

approved

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Last modified May 30 00:42 EDT 2017. Contains 287304 sequences.