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

Author

Leroy Quet, Jul 23 2006

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A007947, A121367, A121369.

Programs

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 *)

Extensions

More terms from Emeric Deutsch, Jul 24 2006

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