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A130802
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a(1) = 1; a(n+1) = Sum_{k=1..n} (a(k)-th integer from among those positive integers which are coprime to (n+1-k)).
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1
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1, 1, 2, 4, 9, 20, 47, 110, 260, 614, 1448, 3421, 8081, 19092, 45107, 106567, 251768, 594816, 1405285, 3320066, 7843851, 18531547, 43781846, 103437135, 244376187, 577352823, 1364029309, 3222597827, 7613573030, 17987504932, 42496516727, 100400469160
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OFFSET
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1,3
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LINKS
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EXAMPLE
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The integers coprime to 5 are 1, 2, 3, 4, 6, ... The a(1)-th=1st of these is 1. The integers coprime to 4 are 1, 3, 5, ... The a(2)-th=1st of these is 1. The integers coprime to 3 are 1, 2, 4, 5, ... The a(3)-th=2nd of these is 2. The integers coprime to 2 are 1, 3, 5, 7, 9, ... The a(4)-th=4th of these is 7. And the integers coprime to 1 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... The a(5)-th=9th of these is 9. So a(6) = 1 + 1 + 2 + 7 + 9 = 20.
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MAPLE
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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), (n-k)), k=1..n-1)) end: seq(a(n), n=1..35); # Alois P. Heinz, Aug 05 2009
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MATHEMATICA
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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], (n - k)], {k, 1, n - 1}]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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