A132274 a(1)=1; a(n+1) = Sum_{k=1..n} (k-th integer from among those positive integers which are coprime to a(n+1-k)).
1, 1, 3, 6, 10, 19, 27, 41, 51, 66, 78, 101, 119, 145, 167, 197, 219, 247, 272, 306, 335, 371, 403, 443, 477, 521, 559, 609, 647, 693, 737, 789, 834, 886, 940, 996, 1055, 1118, 1176, 1243, 1306, 1385, 1450, 1523, 1596, 1676, 1749, 1844, 1914, 2010, 2092, 2188
Offset: 1
Keywords
Examples
The integers coprime to a(1)=1 are 1,2,3,4,5,6,... The 5th of these is 5. The integers coprime to a(2)=1 are 1,2,3,4,5... The 4th of these is 4. The integers coprime to a(3)=3 are 1,2,4,5,7,... The 3rd of these is 4. The integers coprime to a(4)=6 are 1,5,7,11,... The 2nd of these is 5. And the integers coprime to a(5)=10 are 1,3,7,9,11,... The first of these is 1. So a(6) = 5 + 4 + 4 + 5 + 1 = 19.
Programs
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Maple
A132274 := 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 = k then a := a+c ; break; fi; od: od: a; fi; end: seq(A132274(n),n=1..60) ; # R. J. Mathar, Jul 20 2009
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Mathematica
A132274[n_] := A132274[n] = Module[{a, k, an1k, kcoud, c}, If[n == 1, 1, a = 0; For[k = 1, k <= n-1, k++, an1k = A132274[n-k]; kcoud = 0; For[c = 1, True, c++, If[GCD[c, an1k] == 1, kcoud++]; If[kcoud == k, a = a+c; Break[]]]]; a]]; Table[A132274[n], {n, 1, 60}] (* Jean-François Alcover, Jan 28 2024, after R. J. Mathar *)
Extensions
Extended beyond a(8) by R. J. Mathar, Jul 20 2009