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

1,3

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A006530 (largest prime factor), A208884.

Sequence in context: A201757 A053390 A140643 * A108017 A293208 A247364

Adjacent sequences: A331406 A331407 A331408 * A331410 A331411 A331412

Keyword

nonn

Author

Ali Sada, Jan 16 2020

Status

approved