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A007898 Psi_c(n), where Prod_{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

Table of n, a(n) for n=1..68.

F. V. Weinstein, Notes on Fibonacci partitions

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 + ...

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 A114544

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

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Last modified May 27 07:55 EDT 2017. Contains 287202 sequences.