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 A122169 a(1)=1. a(n) = sum of earlier terms, a(k) (1<=k<=n-1), where gcd(a(k),n) is squarefree. 2
 1, 1, 2, 4, 8, 16, 32, 4, 68, 136, 272, 4, 548, 1096, 2192, 4, 4388, 8776, 17552, 4, 35108, 70216, 140432, 4, 280868, 561736, 1123472, 4, 2246948, 4493896, 8987792, 4, 17975588, 35951176, 71902352, 4, 143804708, 287609416, 575218832, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Michel Marcus, Table of n, a(n) for n = 1..1000 EXAMPLE (1,1,2,4,4,4,4,4,4,4,4) is gcd(a(k),12), for 1 <= k <=11. Of these integers, only the first 3 are squarefree, so a(12) = a(1)+a(2)+a(3) = 4. MATHEMATICA sf[n_] := Max @@ Last /@ FactorInteger[n] < 2; f[s_] := Append[s, Plus @@ Select[s, sf[GCD[ #, Length[s] + 1]] &]]; Nest[f, {1}, 40] (* Ray Chandler, Aug 24 2006 *) PROG (PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = sum(k=1, n-1, if (issquarefree(gcd(va[k], n)), va[k])); ); va; } \\ Michel Marcus, Sep 06 2019 CROSSREFS Cf. A122168. Sequence in context: A318776 A036130 A335836 * A114183 A036129 A319303 Adjacent sequences:  A122166 A122167 A122168 * A122170 A122171 A122172 KEYWORD nonn AUTHOR Leroy Quet, Aug 23 2006 EXTENSIONS Extended by Ray Chandler, Aug 24 2006 STATUS approved

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Last modified August 13 19:30 EDT 2020. Contains 336451 sequences. (Running on oeis4.)