A122169 - OEIS

A122169

a(1)=1. a(n) = sum of earlier terms, a(k) (1<=k<=n-1), where gcd(a(k),n) is squarefree.

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