A121368 a(1) = a(2) = 1, a(n) = A007947(a(n-1)) + a(n-2), for n >= 3, i.e., a(n) = a(n-2) plus the largest squarefree divisor of a(n-1).

1, 1, 2, 3, 5, 8, 7, 15, 22, 37, 59, 96, 65, 161, 226, 387, 355, 742, 1097, 1839, 2936, 2573, 5509, 8082, 8203, 16285, 24488, 22407, 46895, 69302, 116197, 185499, 178030, 363529, 541559, 905088, 555701, 1460789, 591330, 2052119, 2643449, 4695568

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..200

Example

6 is the largest squarefree divisor of a(12) = 96. So a(13) = 6 + a(11) = 65.

Maple

with(numtheory): A007947 := proc(n) local i, t1, t2; t1 := ifactors(n)[2]; t2 := mul(t1[i][1], i=1..nops(t1)); end: a:=proc(n) if n=1 or n=2 then 1 else A007947(a(n-1))+a(n-2) fi end: seq(a(n), n=1..25); # Emeric Deutsch, Jul 24 2006

Mathematica

nxt[{a_, b_}]:={b, a+Max[Select[Divisors[b], SquareFreeQ]]}; NestList[nxt, {1, 1}, 50][[All, 1]] (* Harvey P. Dale, Jan 21 2017 *)

Crossrefs

Cf. A007947, A121367, A121369.

Sequence in context: A125727 A112337 A141804 * A010073 A264763 A126167

Adjacent sequences: A121365 A121366 A121367 * A121369 A121370 A121371

Keyword

nonn

Author

Leroy Quet, Jul 23 2006

Extensions

More terms from Emeric Deutsch, Jul 24 2006

More terms from R. J. Mathar, May 18 2007

Status

approved