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

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

Author

Ilya Gutkovskiy, Aug 31 2017

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A056144, A057660, A093820, A287006.

Programs

Maple

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

Mathematica

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}]

Formula

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