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

1,2

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

Links

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

Example

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.

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 *)

Prog

(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<<t; a=concat(a, t)); print1(vecsort(a)", "))}

Crossrefs

Cf. A178480, A178483, A111791.

Sequence in context: A194901 A064470 A194052 * A222758 A127915 A361966

Adjacent sequences: A178481 A178482 A178483 * A178485 A178486 A178487

Keyword

nonn

Author

M. F. Hasler, May 31 2010

Status

approved