OFFSET
1,3
EXAMPLE
To compute a(5) we add the first integer coprime to a(4), the first integer coprime to a(3), the 2nd integer coprime to a(2) and the 4th integer coprime to a(1), which is the first integer in {1,3,4,5,..}, the first integer in {1,2,3,4,...}, the 2nd integer in {1,2,3,4,...} and the 4th integer in {1,2,3,4,..} = 1+1+2+4=8.
MAPLE
A132275 := proc(n) option remember; local a, k, an1k, kcoud, c ; if n = 1 then 1; else a :=0 ; for k from 1 to n-1 do an1k := procname(n-k) ; kcoud := 0 ; for c from 1 do if gcd(c, an1k) = 1 then kcoud := kcoud+1 ; fi; if kcoud = procname(k) then a := a+c ; break; fi; od: od: a; fi; end:
seq(A132275(n), n=1..18) ; # R. J. Mathar, Jul 20 2009
with(numtheory): fc:= proc(t, p) option remember; local m, j, h, pp; if p=1 then t else pp:= phi(p); m:= iquo(t, pp); j:= m*pp; h:= m*p-1; while j<t do h:= h+1; if igcd(p, h)=1 then j:= j+1 fi od; h fi end: a:= proc(n) option remember; `if`(n=1, 1, add(fc(a(k), a(n-k)), k=1..n-1)) end: seq(a(n), n=1..35); # Alois P. Heinz, Aug 05 2009
MATHEMATICA
fc[t_, p_] := fc[t, p] = Module[{m, j, h, pp}, If[p==1, t, pp = EulerPhi[p]; m = Quotient[t, pp]; j = m*pp; h = m*p-1; While[j<t, h++; If [GCD[p, h]==1, j++]]; h]]; a[n_] := a[n] = If[n==1, 1, Sum[fc[a[k], a[n-k]], {k, 1, n-1}]]; Table[a[n], {n, 1, 35}] (* Jean-François Alcover, Mar 21 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Aug 16 2007
EXTENSIONS
Corrected from a(5) on by R. J. Mathar, Jul 21 2009
Extended beyond a(19) Alois P. Heinz, Aug 05 2009
STATUS
approved