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A183010 a(n) = 24n - 1. 22
-1, 23, 47, 71, 95, 119, 143, 167, 191, 215, 239, 263, 287, 311, 335, 359, 383, 407, 431, 455, 479, 503, 527, 551, 575, 599, 623, 647, 671, 695, 719, 743, 767, 791, 815, 839, 863, 887, 911, 935, 959, 983, 1007, 1031, 1055, 1079, 1103, 1127, 1151, 1175, 1199 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is also the denominator of the finite algebraic formula for the number of partitions of n, if n >= 1. The formula is  p(n) = Tr(n)/(24*n - 1), n >= 1. See theorem 1.1 of the Bruinier-Ono paper in the link. For the numerators see A183011.

Bruinier and Ono claim that "the summands are discriminant -24n + 1 singular moduli for a special weak Maass form that we describe in terms of Dedekind's eta-function and Eisenstein series." - Jonathan Vos Post, Jan 26 2011

The sum of the divisors of a(n) is a multiple of 24 [Gupta, Sierpinski]. - Vincenzo Librandi, Apr 07 2011

It appears that a(n) is also the denominator of the coefficient of the third term in the n-th Bruinier-Ono "partition polynomial" H_n(x). See the Bruinier-Ono paper, chapter 5 "Examples". For the numerators see A183007. - Omar E. Pol, Jul 13 2011

Also exponents in the formula q^(-1) + q^23 + 2*q^47 + 3*q^71 + 5*q^95 + 7*q^119 + 11*q^143 + 15*q^167 + ... in which the coefficients are the partition numbers (see A000041, Example section). - Omar E. Pol, Feb 27 2013

LINKS

Table of n, a(n) for n=0..50.

J. H. Bruinier and K. Ono, Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms

A. Dabholkar, S. Murthy, D. Zagier, Quantum Black Holes, Wall Crossing, and Mock Modular Forms, arXiv:1208.4074 [hep-th], 2012-2014, see p. 46.

H. Gupta, Congruent properties of sigma(n), Math. Student 13 (1945) 25-29

E. Larson and L. Rolen, Integrality properties of the CM-values of certain weak Maass forms, arXiv:1107.4114 [math.NT], 2011.

K. Ono, Congruences for the Andrews spt-function, (see 2.1 Producing modular forms)

W. Sierpinski, Elementary Theory of numbers, Monografie Mathematyczne, vol 42 (1964) chapt 4, p. 168

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

a(n) = A008606(n) - 1.

a(1)=23, a(2)=47, a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 23 2011

a(n) = A183011(n)/A000041(n). - Omar E. Pol, Jul 14 2011

24 * A280098(n) = A000203(a(n)) if n>0. - Michael Somos, Dec 25 2016

EXAMPLE

G.f. = -1 + 23*x + 47*x^2 + 71*x^3 + 95*x^4 + 119*x^5 + 143*x^6 + 167*x^7 + ...

MATHEMATICA

Range[23, 2000, 24] (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)

(24*Range[0, 50])-1 (* Harvey P. Dale, Mar 28 2015 *)

PROG

(PARI) a(n)=24*n-1 \\ Charles R Greathouse IV, Jun 14 2011

CROSSREFS

Cf. A000041, A000203, A008606, A134517, A183009, A183011, A187206, A280097, A280098.

Sequence in context: A042044 A042042 A130063 * A134517 A141376 A140614

Adjacent sequences:  A183007 A183008 A183009 * A183011 A183012 A183013

KEYWORD

sign,easy

AUTHOR

Omar E. Pol, Jan 21 2011

STATUS

approved

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Last modified May 30 04:27 EDT 2017. Contains 287305 sequences.