The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A007898 a(n) = psi_c(n), where Product_{k>1} 1/(1-1/k^s)^A007897(k) = Sum_{k>0} psi_c(k)/k^s. 3
 1, 1, 2, 3, 3, 4, 4, 7, 7, 6, 6, 12, 7, 8, 12, 16, 9, 15, 10, 18, 16, 12, 12, 32, 17, 14, 22, 24, 15, 30, 16, 34, 24, 18, 24, 48, 19, 20, 28, 48, 21, 40, 22, 36, 45, 24, 24, 78, 32, 37, 36, 42, 27, 54, 36, 64, 40, 30, 30, 96, 31, 32, 60, 78, 42, 60, 34, 54 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES F. V. Weinstein, The Fibonacci Partitions, preprint, 1995. LINKS F. V. Weinstein, Notes on Fibonacci partitions, arXiv:math/0307150 [math.NT], 2003-2018. EXAMPLE G.f. = x + x^2 + 2*x^3 + 3*x^4 + 3*x^5 + 4*x^6 + 4*x^7 + 7*x^8 + 7*x^9 + ... MATHEMATICA dircon[v_, w_] := Module[{lv = Length[v], lw = Length[w], fv, fw}, fv[n_] := If[n <= lv, v[[n]], 0]; fw[n_] := If[n <= lw, w[[n]], 0]; Table[ DirichletConvolve[fv[n], fw[n], n, m], {m, Min[lv, lw]}]]; a[n_] := Module[{A, v, w, m}, If[n<1, 0, v = Table[Boole[k == 1], {k, n}]; For[k = 2, k <= n, k++, m = Length[IntegerDigits[n, k]] - 1; A = Product[ {p, e} = pe; If[p == 2, If[e<3, e, 2^(e-2) + 2], 1 + p^(e-1) (p-1)/2], {pe, FactorInteger[k]}]; A = (1-x)^-A + x O[x]^m // Normal; w = Table[0, {n}]; For[i = 0, i <= m, i++, w[[k^i]] = Coefficient[A, x, i]]; v = dircon[v, w]]; v[[n]]]]; Array[a, 68] (* Jean-François Alcover, Nov 12 2018, from PARI *) PROG (PARI) {a(n) = my(A, v, w, m, p, e); if( n<1, 0, v = vector(n, k, k==1); for(k=2, n, m = #digits(n, k) - 1; A = factor(k); A = prod( j=1, matsize(A)[1], if( p = A[j, 1], e = A[j, 2]; if( p==2, if( e<3, e, 2^(e-2) + 2), 1 + p^(e-1) * (p-1) / 2))); A = (1 - x)^ -A + x * O(x^m); w = vector(n); for(i=0, m, w[k^i] = polcoeff(A, i)); v = dirmul(v, w)); v[n])}; /* Michael Somos, May 26 2014 */ CROSSREFS Cf. A007896, A007897. Sequence in context: A168173 A095916 A130121 * A110533 A131282 A305296 Adjacent sequences: A007895 A007896 A007897 * A007899 A007900 A007901 KEYWORD nonn AUTHOR Felix Weinstein (wain(AT)ana.unibe.ch) EXTENSIONS New definition by Michel Marcus, May 12 2014 Definition edited by N. J. A. Sloane, May 26 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 26 22:13 EST 2023. Contains 359836 sequences. (Running on oeis4.)