login
A324853
First number divisible by n of its own distinct prime indices.
8
1, 2, 6, 30, 330, 4290, 60060, 1021020, 29609580, 917896980, 33962188260, 1290563153880, 52913089309080, 2275262840290440, 106937353493650680, 6309303856125390120, 422723358360401138040, 30013358443588480800840, 2190975166381959098461320
OFFSET
0,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
a(n) is the first position of n in A324852.
EXAMPLE
a(6) = 60060 = 2^2 * 3 * 5 * 7 * 11 * 13 has prime indices {1,1,2,3,4,5,6}, and is less than any other number divisible by six of its own distinct prime indices.
MATHEMATICA
nn=10000;
With[{mgs=Table[Count[If[n==1, {}, FactorInteger[n]], {p_, _}/; Divisible[n, PrimePi[p]]], {n, nn}]}, Table[Position[mgs, i][[1, 1]], {i, 0, 5}]]
PROG
(C) See Links section.
(PARI) isok(k, n) = {my(f=factor(k)[, 1]); sum(j=1, #f, !(k % primepi(f[j]))) == n; }
a(n) = {my(k=1); while (!isok(k, n), k++); k; } \\ Michel Marcus, Mar 20 2019
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 18 2019
EXTENSIONS
a(8)-a(9) from Rémy Sigrist, Mar 19 2019
a(10)-a(18) from Michel Lagneau, Aug 19 2019
STATUS
approved