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A083561 a(1) = 1 and for n>1: a(n) = n + Max{a(k): k<n, gcd(n,a(k))=1}. 1
1, 3, 4, 7, 12, 13, 20, 21, 29, 39, 50, 41, 63, 55, 56, 79, 96, 97, 116, 117, 137, 159, 182, 161, 207, 233, 260, 261, 289, 319, 350, 351, 383, 417, 452, 419, 489, 527, 566, 567, 608, 569, 651, 695, 653, 741, 788, 743, 837, 887, 938, 939, 992, 941, 1047 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: a(n) ~ n^2/3 as n -> infinity. - Robert Israel, Jun 11 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

N:= 100: # to get a(1)..a(N)

A:= Vector(N): A[1]:= 1:

for n from 2 to N do

  R:= select(t -> igcd(n, A[t])=1, [$1..n-1]);

  A[n]:= n + max(A[R]);

od:

convert(A, list); # Robert Israel, Jun 11 2017

PROG

(PARI) first(n)=my(v=vector(n), t); v[1]=1; for(i=2, n, t=1; for(k=2, i-1, if(gcd(v[k], i)==1 && v[k]>t, t=v[k])); v[i]=t+i); v \\ Charles R Greathouse IV, Jun 12 2017

CROSSREFS

Sequence in context: A300332 A244819 A305185 * A018195 A086417 A051215

Adjacent sequences:  A083558 A083559 A083560 * A083562 A083563 A083564

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jun 12 2003

STATUS

approved

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Last modified July 29 08:13 EDT 2021. Contains 346340 sequences. (Running on oeis4.)