A178484 For n=1,2,... list all numbers not occurring earlier which can be written as a product of the first n primes raised to some nonnegative power less than n.

1, 2, 3, 6, 4, 5, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900, 7, 8, 14, 21, 24, 27, 28, 35, 40, 42, 49, 54, 56, 63, 70, 72, 84, 98, 105, 108, 120, 125, 126, 135, 140, 147, 168, 175, 189, 196, 200, 210, 216, 245, 250, 252

Offset: 1

Author

M. F. Hasler, May 31 2010

Keywords

• nonn

Comments

A condensed version of sequence A178483.

Every positive integer occurs exactly once in this sequence, but depending on its largest prime factor, it may appear later than much larger numbers. E.g. 7=a(29) appears after a(28)=900, and 11=a(257) appears only after a(256)=9261000.

The first n^n terms are the divisors of n#^(n-1), so any term divisible by the k-th prime must appear later than position (k-1)^(k-1). - Charlie Neder, Mar 08 2019

Examples

			n=1 gives a(1) = 1: numbers 2^a with a < 1.
n=2 gives a(2..4) = [2, 3, 6]: numbers 2^a 3^b with a,b < 2.
n=3 gives a(5..28) = [4, 5, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900]: numbers 2^a 3^b 5^c not occurring earlier, with a,b,c < 3.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A178480, A178483, A111791.

Programs

Mathematica

DeleteDuplicates@Flatten@Table[Sort[Times @@ (Prime@Range@n^PadLeft[ IntegerDigits[#, n], n]) & /@ (Range[n^n] - 1)], {n, 2, 4}] (* Ivan Neretin, May 02 2019 *)

PARI

{ s=0; for( L=1,4, a=[]; forvec( v=vector(L,i,[0,L-1]), bittest(s,t=prod( j=1,L,prime(j)^v[L-j+1] )) & next; s+=1<