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URL: https://oeis.org/A256267

⇱ A256267 - OEIS

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A256267
a(n) = A256017(n)/n.
1
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
1,1
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
FORMULA
a(n) = A256017(n)/n.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jun 01 2015
STATUS
approved