A324853 First number divisible by n of its own distinct prime indices.

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.

Links

Table of n, a(n) for n=0..18.

Rémy Sigrist, C program for A324853

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

Crossrefs

Cf. A000720, A001222, A003963, A056239, A120383, A323440.

Cf. A324771, A324846, A324847, A324848, A324849, A324850, A324852, A324856.

Sequence in context: A275593 A120295 A071350 * A329558 A038696 A333373

Adjacent sequences: A324850 A324851 A324852 * A324854 A324855 A324856

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