login
A331409
a(1)=1; for n>1, a(n) = a(n-1)+n, divided by its largest prime factor.
1
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
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
KEYWORD
nonn
AUTHOR
Ali Sada, Jan 16 2020
STATUS
approved