A281680 - OEIS

%I #24 Aug 04 2020 02:10:16

%S 1,1,1,1,3,1,1,3,1,1,3,1,5,3,1,1,3,5,1,3,1,1,3,1,7,3,1,5,3,1,1,3,5,1,

%T 3,1,1,3,7,1,3,1,5,3,1,7,3,5,1,3,1,1,3,1,1,3,1,5,3,7,11,3,5,1,3,1,7,3,

%U 1,1,3,11,5,3,1,1,3,5,1,3,7,1,3,1,13,3,1

%N a(0)=1; for n > 0, if 2n+1 is prime, then a(n)=1, otherwise a(n) = (2n+1)/(largest proper divisor of 2n+1).

%C First occurrence of the k-th prime for k = 2, 3, 4, ... is at n = 4, 12, 24, 60, 84, 144, 180, 264, 420, 480, 684, 840, 924, 1104, etc.; This appears to be either A084921 or A216244. - _Robert G. Wilson v_, Feb 03 2017

%H Robert Israel, <a href="/A281680/b281680.txt">Table of n, a(n) for n = 0..10000</a>

%p f:= proc(n) if isprime(2*n+1) then 1 else min(numtheory:-factorset(2*n+1)) fi end proc:

%p f(0):= 1:

%p map(f, [$0..100]); # _Robert Israel_, Aug 03 2020

%t f[n_] := If[ PrimeQ[2n +1], 1, FactorInteger[2n +1][[1, 1]]]; f[0] = 1; Array[f, 87, 0] (* _Robert G. Wilson v_, Jan 31 2017 *)

%o (PARI) a(n) = if (n==0, 1, if (isprime(o=2*n+1), 1, d=divisors(o); o/d[#d-1])); \\ _Michel Marcus_, Feb 02 2017

%Y Cf. A032742, A281681.

%K nonn

%O 0,5

%A _Enrique Navarrete_, Jan 26 2017