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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; text; 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

Table of n, a(n) for n=3..48.

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.

EXTENSIONS

More terms from Vladeta Jovovic, Nov 11 2001

STATUS

approved

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Last modified June 22 23:15 EDT 2017. Contains 288633 sequences.