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A060186 Generalized sum of divisors function: third diagonal of A060184. 2
1, 0, 1, 0, 5, -1, 5, -2, 9, 3, 9, -2, 14, -1, 15, 10, 15, 7, 11, 14, 10, 26, 20, 28, 2, 41, -5, 63, -21, 82, -5, 91, -49, 122, -46, 139, -84, 165, -74, 240, -147, 242, -142, 290, -217, 333, -189, 378, -284, 463, -290, 508, -408, 560, -377 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,5

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.

LINKS

Table of n, a(n) for n=3..57.

FORMULA

G.f.: (t(1)^3-3*t(1)*t(2)+2*t(3))/6 where t(i) = Sum((x^n/(1+x^(n)))^i,n=1..inf), i=1..3. - Vladeta Jovovic, Sep 20 2007

MAPLE

mufact := proc(k, sumax) local res, c, i, j, isord, s ; res := [] ; for s from k*(k+1)/2 to sumax do c := combinat[composition](s, k) ; for j from 1 to nops(c) do isord := true ; for i from 2 to nops(op(j, c)) do if op(i, op(j, c))<= op(i-1, op(j, c)) then isord := false ; fi ; od ; if isord then res := [op(res), op(j, c)] ; fi ; od ; od ; RETURN(res) ; end: qm := proc(gfpart, n) local f, i ; f := q^add(op(i, gfpart), i=1..nops(gfpart)) ; for i from 1 to nops(gfpart) do f := taylor(f/(1+q^op(i, gfpart)), q=0, n+1) ; od ; RETURN(f) ; end: A060186 := proc(n) local k, ms, gf, gfpart, i ; k := 3 ; ms := mufact(k, n) ; gf := 0; for i from 1 to nops(ms) do gfpart := op(i, ms) ; gf := taylor(gf+qm(gfpart, n), q=0, n+1) ; od ; RETURN(gf) ; end: nmax := 60 : a := A060186(nmax) : for n from 6 to nmax do printf("%d, ", coeftayl(a, q=0, n)) ; od ; # R. J. Mathar, Jun 26 2007

MATHEMATICA

max = 60; t[i_] := Sum[(x^n/(1 + x^(n)))^i, {n, 1, max}]; s = Series[(t[1]^3 - 3*t[1]*t[2] + 2*t[3])/6, {x, 0, max+1}]; a[n_] := SeriesCoefficient[s, {x, 0, n}]; Table[a[n], {n, 6, max}] (* Jean-François Alcover, Jan 17 2014, after Vladeta Jovovic *)

CROSSREFS

Sequence in context: A055191 A299628 A217774 * A240995 A122002 A228639

Adjacent sequences:  A060183 A060184 A060185 * A060187 A060188 A060189

KEYWORD

easy,sign

AUTHOR

N. J. A. Sloane, Mar 19 2001

EXTENSIONS

More terms from R. J. Mathar, Jun 26 2007

STATUS

approved

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Last modified December 17 06:45 EST 2018. Contains 318192 sequences. (Running on oeis4.)