A256267 - OEIS

%I #25 Sep 09 2017 23:27:11

%S 2,2,3,2,5,3,7,2,3,5,11,13,13,7,5,2,17,3,19,5,7,11,23,29,5,13,3,7,29,

%T 31,31,2,11,17,7,37,37,19,13,41,41,7,43,11,47,23,47,53,7,5,17,13,53,3,

%U 11,59,19,29,59,61,61,31,67,2,13,11,67,17,23,71,71,73

%N a(n) = A256017(n)/n.

%C A256017(n) is the least integer k > n such that all divisors of n are exactly the first divisors of k in increasing order. a(n) is the ratio A256017(n)/n. This ratio is a prime number.

%C a(p)=p if p prime;

%C a(n)=2 if n is a power of 2;

%C a(n)=3 if n = 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, ... (A038754);

%C a(n)=5 if n = 5, 10, 15, 20, 25, 50, ... (A140730);

%C a(n)=7 if n = 7, 14, 21, 28, 35, 42, 49, 98, 147, 196, 245, ...

%H Michel Lagneau, <a href="/A256267/b256267.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A256017(n)/n.

%t a[n_]:=If[n==1, 2, Block[{k= 2*n, f, d, m}, f = FactorInteger @n; If[1 == Length@f, f[[1, 1]]^(1 + f[[1, 2]]), d = Divisors@ n; m = Length@ d; While[ Take[ Divisors@ k, m] != d, k += n]; k]]]/n; Array[a, 100](* program from _Giovanni Resta_, adapted for this sequence. See A256017 *)

%Y Cf. A038754, A140730, A256017.

%K nonn

%O 1,1

%A _Michel Lagneau_, Jun 01 2015