%I #21 Oct 27 2019 17:31:39

%S 240,270,300,330,360,390,630,660,690,720,750,780,810,1050,1080,1110,

%T 1140,1170,1200,1230,1500,1530,1560,1590,1620,1650,1890,1920,1950,

%U 1980,2010,2040,2070,2550,2580,2610,2640,2670,2700,2940,2970,3000,3030,3060,3090,3120,3360,3390,3420,3450,3480,3510,3540,3810,3840,3870,3900,3930,3960,4200

%N Numbers n that are multiples of 6 and for which A257993(A276086(A276086(n))) is larger than A257993(n), where A276086 converts the primorial base expansion of n into its prime product form, and A257993 returns the index of the least prime not present in its argument.

%C Multiples of six such that the least nondivisor prime of the original n is less than the least nondivisor prime of the number obtained after two iterations of A276086 is.

%C All terms are multiples of 5 (and thus of 30), because when applied to any number which is a multiple of 6, but not of 5 (and thus not a multiple of 30, so the primorial expansion ends with "x00", where x <> 0, and A257993(n) = 3), A276086 will yield a number of the form 30k+5 or 30k+25 (A084967) whose primorial expansion ends either as "...021" or as "...401" (with the least significant zero either in position 2 or 3), thus then A328578(n) = A257993(A276086(A276086(n))) is definitely not larger than 3, while A257993(6k) >= 3 for all k >= 1.

%H Antti Karttunen, <a href="/A328589/b328589.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%o (PARI)

%o A257993(n) = { for(i=1,oo,if(n%prime(i),return(i))); }

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A328578(n) = A257993(A276086(A276086(n)));

%o isA328589(n) = ((!(n%6))&&(A328578(n) > A257993(n)));

%Y Subsequence of A328588.

%Y Other multiples of 6 are either in A328586 or in A328587.

%Y Cf. A049345, A084967, A257993, A276086, A328578, A328585, A328588, A328590, A328762.

%K nonn

%O 1,1

%A _Antti Karttunen_, Oct 21 2019