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A132275 a(1)=1. a(n+1) = sum{k=1 to n} (a(k)th integer from among those positive integers which are coprime to a(n+1-k)). 4
1, 1, 2, 4, 8, 17, 37, 81, 177, 387, 847, 1856, 4066, 8910, 19524, 42783, 93760, 205475, 450282, 986770, 2162473, 4738974, 10385267, 22758885, 49875175, 109299427, 239525260, 524909877, 1150318695, 2520876742, 5524399079, 12106496388, 26530895539, 58141380910 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..34.

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-Fran├žois Alcover, Mar 21 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A126572, A132273, A132274.

Sequence in context: A076892 A106462 A129987 * A136671 A274114 A024557

Adjacent sequences:  A132272 A132273 A132274 * A132276 A132277 A132278

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

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Last modified April 3 21:54 EDT 2020. Contains 333207 sequences. (Running on oeis4.)