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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).
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
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
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