A050366 Number of ways to write n as an lterm, where an lterm is an unordered sum which is either 2, or 1 + an ordered product of lterms.

1, 1, 1, 2, 2, 4, 4, 7, 8, 12, 12, 21, 21, 29, 33, 46, 46, 67, 67, 93, 101, 125, 125, 177, 181, 223, 238, 300, 300, 394, 394, 488, 512, 604, 620, 796, 796, 930, 972, 1182, 1182, 1450, 1450, 1712, 1804, 2054, 2054, 2510, 2526, 2924, 3016, 3483, 3483

Offset

2,4

Links

Michael De Vlieger, Table of n, a(n) for n = 2..10000

Formula

Shifts left under transform T where Ta has Dirichlet g.f.: 1/(1-A(s)).

Example

The different ways of writing the numbers 2 through 7 as lterms are:
  2 = 2,
  3 = 1 + 2,
  4 = 1 + (1+2),
  5 = 1 + (1+1+2) = 1 + 2*2,
  6 = 1 + (1+1+1+2) = 1 + (1+2*2),
  7 = 1 + (1+1+1+1+2) = 1 + (1+1+2*2) = 1 + 2*(1+2) = 1 + (1+2)*2.

Mathematica

Fold[Function[{a, n}, Append[a, DivisorSum[n, a[[#]] a[[n/# - 1]] &, # < n &]]], {1}, Range[2, 53]] (* Michael De Vlieger, Mar 14 2018 *)

Prog

(PARI) a(n)=if(n<2, 1, sumdiv(n, d, if(d<n, a(d)*a(n/d-1), 0))) \\ Benoit Cloitre, Mar 13 2018

Crossrefs

Cf. A002033, A050318, A050319, A050365.

Sequence in context: A035944 A227134 A240013 * A332753 A027591 A027596

Adjacent sequences: A050363 A050364 A050365 * A050367 A050368 A050369

Keyword

nonn,eigen

Author

Christian G. Bower, Oct 15 1999

Status

approved