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A130025
a(1)=1; a(n) = a(n-1) + (number of terms, from among terms a(1) through a(n-1), which are squarefree).
1
1, 2, 4, 6, 9, 12, 15, 19, 24, 29, 35, 42, 50, 58, 67, 77, 88, 99, 110, 122, 135, 148, 161, 175, 189, 203, 218, 234, 250, 266, 283, 301, 320, 339, 359, 380, 401, 423, 445, 468, 491, 515, 540, 565, 591, 618, 646, 675, 704, 733, 763, 794, 826, 859, 893, 928, 963
OFFSET
1,2
LINKS
EXAMPLE
Among the first 8 terms of the sequence there are 5 squarefree integers (1,2,6,15,19). So a(9) = a(8) + 5 = 24.
MAPLE
with(numtheory): a[1] := 1: for n from 2 to 60 do ct := 0: for j to n-1 do if abs(mobius(a[j])) > 0 then ct := ct+1 else ct := ct end if end do: a[n] := a[n-1]+ct end do: seq(a[n], n = 1 .. 60); # Emeric Deutsch, Jul 18 2007
MATHEMATICA
nxt[{t_, a_}]:={If[SquareFreeQ[t+a], 1, 0]+t, t+a}; Transpose[NestList[nxt, {1, 1}, 60]][[2]] (* Harvey P. Dale, Jan 04 2015 *)
CROSSREFS
Sequence in context: A194201 A194203 A261222 * A278299 A145802 A076271
KEYWORD
nonn
AUTHOR
Leroy Quet, Jun 20 2007
EXTENSIONS
More terms from Emeric Deutsch and Joshua Zucker, Jul 18 2007
STATUS
approved