A256267 a(n) = A256017(n)/n.

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

Offset: 1

Author

Michel Lagneau, Jun 01 2015

Keywords

• nonn

Comments

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.

a(p)=p if p prime;

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

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

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

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

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A038754, A140730, A256017.

Programs

Mathematica

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 *)

Formula

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