A093820 -id:A093820 - cp's OEIS frontend

A056144 a(1) = 1, a(m+1) = Sum_{k=1..m} gcd(m, a(k)).

1, 1, 2, 3, 5, 9, 11, 7, 9, 27, 15, 21, 25, 13, 27, 49, 17, 33, 59, 19, 33, 69, 53, 45, 47, 61, 39, 117, 47, 29, 89, 31, 33, 161, 51, 75, 105, 37, 57, 159, 65, 41, 135, 43, 85, 251, 91, 139, 89, 127, 127, 171, 113, 157, 199, 131, 93, 227, 87, 117, 185, 121, 123, 227, 65

Offset: 1

Leroy Quet, Aug 04 2000

From Ivan Neretin, Apr 06 2016: (Start)
a(n) >= n-1.
All terms except a(3) = 2 are odd.
For all n of the form 2^k+1 except 3, a(n) = n.
(End)

			a(7) = gcd(6,1) + gcd(6,1) + gcd(6,2) + gcd(6,3) + gcd(6,5) + gcd(6,9) = 1 + 1 + 2 + 3 + 1 + 3 = 11.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A093820.

a:= proc(n) option remember;
      1+add(igcd(n-1, a(j)), j=2..n-1)
    end:
seq(a(n), n=1..65);  # Alois P. Heinz, Mar 06 2025

Fold[Append[#1, Total@GCD[#1, #2]] &, {1}, Range@64] (* Ivan Neretin, Apr 06 2016 *)

A286946 a(1) = 1; a(n+1) = Sum_{k=1..n} a(n)/gcd(a(k),a(n)).

Original entry on oeis.org

1, 1, 2, 5, 16, 57, 286, 1431, 9064, 51398, 359787, 3118155, 25568872, 223727631, 2311852188, 15990310968, 105935810164, 1038449718056, 10903722039589, 185715007642033, 3528585145198628, 46753753173881822, 658243630211230916, 9215410822957232825, 197209791611284782456, 2112570763708981231112

Offset: 1

Ilya Gutkovskiy, Aug 31 2017

nonn

			a(1) = 1;
a(2) = a(1)/gcd(a(1),a(1)) = 1/gcd(1,1) = 1;
a(3) = a(2)/gcd(a(1),a(2)) + a(2)/gcd(a(2),a(2)) = 1/gcd(1,1) + 1/gcd(1,1) = 2;
a(4) = a(3)/gcd(a(1),a(3)) + a(3)/gcd(a(2),a(3)) + a(3)/gcd(a(3),a(3)) = 2/gcd(1,2) + 2/gcd(1,2) + 2/gcd(2,2) = 5, etc.

Robert Israel, Table of n, a(n) for n = 1..481
Index entries for sequences related to lcm's

Cf. A056144, A057660, A093820, A287006.

A[1]:= 1:
for n from 1 to 50 do
  A[n+1]:= add(A[n]/igcd(A[k],A[n]),k=1..n)
od:
seq(A[i],i=1..50); # Robert Israel, Sep 01 2017

a[1] = 1; a[n_] := a[n] = Sum[a[n - 1]/GCD[a[k - 1], a[n - 1]], {k, 2, n}]; Table[a[n], {n, 26}]
a[1] = 1; a[n_] := a[n] = Sum[LCM[a[k - 1], a[n - 1]]/a[k - 1], {k, 2, n}]; Table[a[n], {n, 26}]

a(1) = 1; a(n+1) = Sum_{k=1..n} lcm(a(k),a(n))/a(k).

cp's OEIS Frontend

A056144 a(1) = 1, a(m+1) = Sum_{k=1..m} gcd(m, a(k)).

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