A331409 a(1)=1; for n>1, a(n) = a(n-1)+n, divided by its largest prime factor.

1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 4, 8, 3, 1, 8, 8, 5, 1, 4, 8, 1, 1, 8, 16, 1, 9, 12, 8, 1, 1, 16, 16, 7, 1, 12, 16, 1, 3, 6, 2, 1, 1, 4, 16, 1, 1, 16, 32, 27, 7, 2, 18, 1, 5, 12, 4, 1, 1, 12, 24, 5, 1, 32, 32, 1, 1, 4, 24, 3, 1, 24, 32, 15, 1, 4, 16, 3, 27, 2, 2, 1, 1, 12, 32, 9

Offset: 1

Author

Ali Sada, Jan 16 2020

Keywords

• nonn

Examples

			For n=4, a(4) = 2+4 divided by its largest prime factor = 6/3 = 2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530 (largest prime factor), A208884.

Programs

Magma

[n eq 1 select 1 else (Self(n-1)+n) div Max(PrimeDivisors(Self(n-1)+n)): n in [1..85]]; // Marius A. Burtea, Feb 17 2020

Mathematica

f[n_] := n/FactorInteger[n][[-1, 1]]; a[1] = 1; a[n_] := a[n] = f[a[n - 1] + n]; Array[a, 100] (* Amiram Eldar, Jan 16 2020 *)
nxt[{n_,a_}]:={n+1,(a+n+1)/FactorInteger[a+n+1][[-1,1]]}; NestList[nxt,{1,1},90][[All,2]] (* Harvey P. Dale, Nov 12 2022 *)

PARI

a(n) = if (n==1, 1, my(x=a(n-1)+n); x/vecmax(factor(x)[,1])); \\ Michel Marcus, Feb 20 2020