OFFSET
1,1
COMMENTS
Brown shows that this sequence has density 0 and is a subsequence of A013929. Mei shows that in fact it is a subsequence of A048108. - Charles R Greathouse IV, Jun 07 2013
Not a subsequence of A025487: 80, 108, 112, etc. are not the product of primorials. - Charles R Greathouse IV, Jun 07 2013
The product of any exceptional numbers is an exceptional number. - Thomas Ordowski, Jun 14 2015
Grost proved that p^k is in the sequence if and only if 2^p < prime(k), where p is a prime. - Thomas Ordowski, Jun 15 2015
Only very few of the initial terms, {108, 162, 243, 324, 486, 729, ...} are not multiples of 8. Note that the 2nd to 6th in this list (and certainly more) equal 81*k = (10 + 1/8)*a(n) with n = 2, 3, 4, 5, 7, ... - M. F. Hasler, Jun 15 2022
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Ron Brown, The minimal number with a given number of divisors (2009), Journal of Number Theory 116:1 (2005), pp. 150-158.
M. E. Grost, The smallest number with a given number of divisors, Amer. Math. Monthly, 75 (1968), 725-729.
Shu-Yuan Mei, A new class of ordinary integers, video summary of article.
Shu-Yuan Mei, A new class of ordinary integers, Journal of Number Theory, Volume 133, Issue 10, October 2013, Pages 3559-3564.
Anna K. Savvopoulou and Christopher M. Wedrychowicz, On the smallest number with a given number of divisors, The Ramanujan Journal, 2015, Vol. 37, pp. 51-64.
EXAMPLE
m=8 is a term: A005179(8) = 2^3 * 3 = 24 < 30 = 2^1 * 3^1 * 5^1 = A037019(8). - Jon E. Schoenfield, Mar 18 2022
PROG
(PARI) select( {is_A072066(n)=A005179(n)<A037019(n)}, [1..9999]) \\ M. F. Hasler, Oct 14 2014, updated Jun 15 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
David Wasserman, Jun 12 2002
EXTENSIONS
Links updated by Michel Marcus and M. F. Hasler, Oct 14 2014
STATUS
approved