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A000499 a(n) = Sum_{k=1..n-1} k^3*sigma(k)*sigma(n-k).
(Formerly M5193 N2257)
3
0, 1, 27, 184, 875, 2700, 7546, 17600, 35721, 72750, 126445, 223776, 353717, 595448, 843750, 1349120, 1827636, 2808837, 3600975, 5306000, 6667920, 9599172, 11509982, 16416000, 19015625, 26605670, 30902310, 41686848, 46948825, 64233000, 70306760, 94089216 (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

John Cerkan, Table of n, a(n) for n = 1..10000

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^3*sigma(k)*sigma(n-k). - Michel Marcus, Feb 02 2014

EXAMPLE

G.f. = x^2 + 27*x^3 + 184*x^4 + 875*x^5 + 2700*x^6 + 7546*x^7 + 17600*x^8 + ...

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(3);

MATHEMATICA

a[n_] := Sum[k^3*DivisorSigma[1, k]*DivisorSigma[1, n - k], {k, 1, n - 1}]; Array[a, 32] (* Jean-Fran├žois Alcover, Feb 09 2016 *)

PROG

(PARI) a(n) = sum(k=1, n-1, k^3*sigma(k)*sigma(n-k)); \\ Michel Marcus, Feb 02 2014

CROSSREFS

Cf. A000441, A000477.

Sequence in context: A224454 A258637 A228463 * A042416 A216108 A216110

Adjacent sequences:  A000496 A000497 A000498 * A000500 A000501 A000502

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms and 0 prepended by Michel Marcus, Feb 02 2014

STATUS

approved

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Last modified May 28 16:24 EDT 2017. Contains 287241 sequences.