|
| |
|
|
A002127
|
|
MacMahon's generalized sum of divisors function.
(Formerly M2770 N1114)
|
|
1
| |
|
|
1, 3, 9, 15, 30, 45, 67, 99, 135, 175, 231, 306, 354, 465, 540, 681, 765, 945, 1040, 1305, 1386, 1695, 1779, 2205, 2290, 2754, 2835, 3438, 3480, 4185, 4272, 5076, 5004, 6100, 5985, 7155, 7154, 8325, 8190, 9840, 9471, 11241, 11055, 12870, 12420, 14911
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 3,2
|
|
|
REFERENCES
| P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., (2) 19 (1919), 75-113; Coll. Papers II, pp. 303-341.
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).
|
|
|
LINKS
| G. E. Andrews and S. C. F. Rose, MacMahon's sum-of-divisors functions, Chebyshev polynomials, and Quasi-modular forms
S. Rose, What literature is known about MacMahon's generalized sum-of-divisors function?
|
|
|
FORMULA
| G.f.: (Sum_{k>=0} (-1)^k * (2*k + 1) * binomial( k+2, 4) * x^( k*(k+1) / 2 )) / (5 * Sum_{k>=0} (-1)^k * (2*k + 1) * x^( k*(k+1) / 2 )). - Michael Somos, Jan 10 2012
|
|
|
EXAMPLE
| x^3 + 3*x^4 + 9*x^5 + 15*x^6 + 30*x^7 + 45*x^8 + 67*x^9 + 99*x^10 + ...
|
|
|
PROG
| (PARI) {a(n) = if( n<1, 0, ( sigma( n, 3) - (2*n - 1) * sigma(n) ) / 8)} /* Michael Somos, Jan 10 2012 */
|
|
|
CROSSREFS
| A diagonal of A060043.
Sequence in context: A122819 A056287 A099409 * A061810 A048701 A031159
Adjacent sequences: A002124 A002125 A002126 * A002128 A002129 A002130
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 11 2001
|
| |
|
|
