A331409 - OEIS

%I #23 Nov 12 2022 18:22:29

%S 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,

%T 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,

%U 1,32,32,1,1,4,24,3,1,24,32,15,1,4,16,3,27,2,2,1,1,12,32,9

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

%H Rémy Sigrist, <a href="/A331409/b331409.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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 *)

%t 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 *)

%o (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

%o (PARI) a(n) = if (n==1, 1, my(x=a(n-1)+n); x/vecmax(factor(x)[,1])); \\ _Michel Marcus_, Feb 20 2020

%Y Cf. A006530 (largest prime factor), A208884.

%K nonn

%O 1,3

%A _Ali Sada_, Jan 16 2020