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, 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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Adjacent sequences: A130022 A130023 A130024 * A130026 A130027 A130028

Keyword

nonn

Author

Leroy Quet, Jun 20 2007

Extensions

More terms from Emeric Deutsch and Joshua Zucker, Jul 18 2007

Status

approved