A281680 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).

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, 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, 1, 1, 3, 11, 5, 3, 1, 1, 3, 5, 1, 3, 7, 1, 3, 1, 13, 3, 1

Offset

0,5

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Maple

f:= proc(n) if isprime(2*n+1) then 1 else min(numtheory:-factorset(2*n+1)) fi end proc:
f(0):= 1:
map(f, [$0..100]); # Robert Israel, Aug 03 2020

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A032742, A281681.

Sequence in context: A101685 A238737 A049653 * A377864 A060266 A073310

Adjacent sequences: A281677 A281678 A281679 * A281681 A281682 A281683

Keyword

nonn

Author

Enrique Navarrete, Jan 26 2017

Status

approved