A121367 a(1) = a(2) = 1, a(n) = a(n-1) + A007947(a(n-2)) for n >= 3, i.e., a(n) = a(n-1) plus the largest squarefree divisor of a(n-2).

1, 1, 2, 3, 5, 8, 13, 15, 28, 43, 57, 100, 157, 167, 324, 491, 497, 988, 1485, 1979, 2144, 4123, 4257, 8380, 9799, 13989, 23788, 37777, 49671, 87448, 104005, 125867, 229872, 355739, 384473, 740212, 1124685, 1494791, 1536446, 3031237, 4567683, 7598920

Offset

1,3

Links

Table of n, a(n) for n=1..42.

Example

14 is the largest squarefree divisor of a(9) = 28. So a(11) = a(10) + 14 = 57.

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 a(n-1)+A007947(a(n-2)) fi end: seq(a(n), n=1..20); # Emeric Deutsch, Jul 24 2006

Mathematica

nxt[{a_, b_}]:={b, b+Max[Select[Divisors[a], SquareFreeQ]]}; Transpose[ NestList[ nxt, {1, 1}, 50]][[1]] (* Harvey P. Dale, Jul 23 2015 *)

Crossrefs

Cf. A007947, A121368, A121369.

Sequence in context: A138183 A076591 A078695 * A308495 A221672 A241551

Adjacent sequences: A121364 A121365 A121366 * A121368 A121369 A121370

Keyword

nonn

Author

Leroy Quet, Jul 23 2006

Extensions

More terms from Emeric Deutsch, Jul 24 2006

More terms from R. J. Mathar, May 11 2007

Status

approved