A133902 a(n) = a(n-1)* d(n) if gcd(n,a(n-1))=1, otherwise a(n) = a(n-1)/gcd(n,a(n-1)). Here gcd(n,a(n-1)) is greatest common divisor, d(n) is number of divisors.

1, 1, 2, 4, 1, 2, 1, 2, 1, 3, 12, 24, 2, 4, 2, 8, 1, 2, 1, 2, 1, 4, 2, 4, 1, 3, 12, 4, 1, 2, 1, 2, 1, 4, 2, 8, 2, 4, 2, 8, 1, 2, 1, 2, 1, 6, 3, 6, 1, 3, 18, 6, 3, 6, 1, 4, 1, 4, 2, 4, 1, 2, 1, 6, 3, 12, 2, 4, 1, 4, 2, 4, 1, 2, 1, 6, 3, 12, 2, 4, 1, 5, 20, 40, 10, 2, 1, 4, 1, 2, 1, 4, 1, 4, 2, 8

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Maple

A[0]:= 1:
for n from 1 to 1000 do
  g:= igcd(n, A[n-1]);
  if g = 1 then A[n]:= A[n-1]*numtheory:-tau(n) else A[n]:= A[n-1]/g fi
od:
seq(A[i], i=0..1000); # Robert Israel, Aug 10 2020

Mathematica

Nest[Append[#1, If[#3 == 1, Last[#1]*DivisorSigma[0, #2], Last[#1]/#3]] & @@ {#1, #2, GCD[Last[#1], #2]} & @@ {#, Length[#] + 1} &, {1, 1}, 93] (* Michael De Vlieger, Mar 21 2022 *)

Crossrefs

Cf. A000005, A034444, A001222.

Sequence in context: A103161 A338000 A030420 * A265823 A305717 A208645

Adjacent sequences: A133899 A133900 A133901 * A133903 A133904 A133905

Keyword

nonn

Author

Ctibor O. Zizka, Jan 07 2008

Extensions

Corrected, extended and offset changed by Robert Israel, Aug 10 2020

Status

approved