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A003318 a(n + 1) = 1 + a( floor(n/1) ) + a( floor(n/2) ) + ... + a( floor(n/n) ).
(Formerly M1052)
3
1, 2, 4, 7, 12, 18, 28, 39, 55, 74, 100, 127, 167, 208, 261, 322, 399, 477, 581, 686, 820, 967, 1142, 1318, 1545, 1778, 2053, 2347, 2697, 3048, 3486, 3925, 4441, 4986, 5610, 6250, 7024, 7799, 8680, 9604, 10673, 11743, 13008, 14274, 15718, 17239, 18937, 20636 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Partial sums of A003238. - Emeric Deutsch, Dec 17 2014

REFERENCES

Goldberg, M. K.; Livshits, E. M.; Minimal universal trees. (Russian) Mat. Zametki 4 1968 371-379.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

R. C. Read, personal communication.

LINKS

Joerg Arndt, Table of n, a(n) for n = 1..1000

M. K. Gol'dberg, É. M. Livshits, On minimal universal trees, Mathematical notes of the Academy of Sciences of the USSR, September 1968, Volume 4, Issue 3, pp 713-717, translated from Matematicheskie Zametki, Vol. 4, No. 3, pp. 371-379, September, 1968.

R. C. Read, Letter to N. J. A. Sloane and notes, May 1974

MAPLE

A[1]:= 1;

for n from 1 to 99 do

  A[n+1]:= 1 + add(A[floor(n/k)], k=1..n)

od:

seq(A[n], n=1..100); # Robert Israel, Aug 24 2014

PROG

(PARI) N=1001;

v=vector(N, n, n==1);

for(n=1, N-1, v[n+1]=1 + sum(k=1, n, v[floor(n/k)]) );

for(n=1, N, print(n, " ", v[n])); \\ b-file

\\ Joerg Arndt, Aug 25 2014

CROSSREFS

Cf. A003238 (first differences).

Sequence in context: A175812 A002621 A033500 * A035300 A035296 A230118

Adjacent sequences:  A003315 A003316 A003317 * A003319 A003320 A003321

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 16 01:19 EDT 2019. Contains 328038 sequences. (Running on oeis4.)