A130802 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)).

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

Offset: 1

Author

Leroy Quet, Aug 20 2007

Keywords

• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..800

Crossrefs

Cf. A132273, A132274, A132275.

Programs

Maple

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 jAlois 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], (n - k)], {k, 1, n - 1}]];
Array[a, 35] (* Jean-François Alcover, Nov 19 2020, after Alois P. Heinz *)

Extensions

More terms from Alois P. Heinz, Aug 05 2009