OFFSET
1,2
COMMENTS
Also numbers with the k first prime numbers in their prime tower factorization, without duplicate, for some k (see A182318 for the definition of the prime tower factorization of a number).
This sequence contains the primorial numbers (A002110); 8 = 2^3 is the first term in this sequence that is not a primorial number.
This sequence contains A260548.
All terms belong to A284763.
If a(n) <= p# for some prime p, then a(n) is p-smooth (p# denotes the product of the primes <= p, see A002110).
There are A000272(k+1) terms with k prime numbers in their prime tower factorization:
- for k=0: 1,
- for k=1: 2,
- for k=2: 2*3, 2^3, 3^2,
- for k=3: 2*3*5, 2^3*5, 2^5*3, 3^2*5, 3^5*2, 5^2*3, 5^3*2, 2^(3*5), 3^(2*5), 5^(2*3), 2^3^5, 2^5^3, 3^2^5, 3^5^2, 5^2^3, 5^3^2.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..500
Rémy Sigrist, Illustration of the first terms
EXAMPLE
1626625 = 5^3*7*11*13^2 appears in this sequence.
PROG
(PARI) isprimorial(n) = if (n==1, 1, my (f=factor(n)); (#f~ == primepi(vecmax(f[, 1]))) && (vecmax(f[, 2]) == 1));
a279513(n) = my (f=factor(n)); prod(i=1, #f~, f[i, 1]*a279513(f[i, 2]));
isok(n) = isprimorial(a279513(n)); \\ Michel Marcus, Apr 08 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Apr 05 2017
STATUS
approved