|
|
A316476
|
|
Stable numbers. Numbers whose distinct prime indices are pairwise indivisible.
|
|
64
|
|
|
1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 43, 45, 47, 49, 51, 53, 55, 59, 61, 64, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 89, 91, 93, 95, 97, 99, 101, 103, 107, 109, 113, 119, 121, 123, 125, 127, 128, 131, 135, 137
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
A prime index of n is a number m such that prime(m) divides n.
|
|
LINKS
|
|
|
EXAMPLE
|
The prime indices of 45 are {2,2,3}, so the distinct prime indices are {2,3}, which are pairwise indivisible, so 45 belongs to the sequence.
The prime indices of 105 are {2,3,4}, which are not pairwise indivisible (2 divides 4), so 105 does not belong to the sequence.
|
|
MATHEMATICA
|
Select[Range[100], Select[Tuples[If[#===1, {}, Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]]], 2], UnsameQ@@#&&Divisible@@#&]=={}&]
|
|
PROG
|
(PARI) ok(n)={my(v=apply(primepi, factor(n)[, 1])); for(j=2, #v, for(i=1, j-1, if(v[j]%v[i]==0, return(0)))); 1} \\ Andrew Howroyd, Aug 26 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|