A316476 - OEIS

%I #14 Nov 27 2024 17:57:04

%S 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,

%T 45,47,49,51,53,55,59,61,64,67,69,71,73,75,77,79,81,83,85,89,91,93,95,

%U 97,99,101,103,107,109,113,119,121,123,125,127,128,131,135,137

%N Stable numbers. Numbers whose distinct prime indices are pairwise indivisible.

%C A prime index of n is a number m such that prime(m) divides n.

%H Andrew Howroyd, <a href="/A316476/b316476.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>

%e 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.

%e 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.

%t Select[Range[100],Select[Tuples[If[#===1,{},Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]]],2],UnsameQ@@#&&Divisible@@#&]=={}&]

%o (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

%Y Cf. A056239, A112798, A285572, A285573, A303362, A304713, A316468, A316475, A327393, A327394, A378442 (characteristic function).

%K nonn

%O 1,2

%A _Gus Wiseman_, Jul 04 2018