A260815 a(2) = 3; for n >= 3, a(n) = a(n-1) + gcd(n, a(n-1))^2.

3, 12, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 575, 576, 577, 578, 579, 580, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 1430, 1599, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 1610, 1611, 1612

Offset: 2

Author

Arkadiusz Wesolowski, Jul 31 2015

Keywords

• nonn
• look

Comments

The first differences of a(n) are all squares.

Examples

			a(3) = 3 + gcd(3, 3)^2 = 3 + 9 = 12.
a(4) = 12 + gcd(4, 12)^2 = 12 + 16 = 28.
a(5) = 28 + gcd(5, 28)^2 = 28 + 1 = 29.
		

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A167195, A343402.

Programs

Magma

I:=[0, 3]; Remove([n le 2 select I[n] else Self(n-1)+Gcd(n, Self(n-1))^2: n in [1..52]], 1);

Maple

N:= 100: # for a(2)..a(N)
A:= Array(2..N):
A[2]:= 3:
for n from 3 to N do
  A[n]:= A[n-1]+igcd(n,A[n-1])^2
od:
seq(A[i],i=2..N); # Robert Israel, Apr 13 2021

Mathematica

Nest[Append[#1, #1[[-1]] + GCD[#2, #1[[-1]]]^2] & @@ {#, Length[#] + 2} &, {3}, 50] (* Michael De Vlieger, Apr 13 2021 *)