A284889 Numbers n such that A279513(n) is a primorial number (A002110).

1, 2, 6, 8, 9, 30, 40, 45, 75, 96, 210, 250, 280, 315, 486, 525, 672, 735, 1750, 1920, 2310, 3080, 3402, 3430, 3465, 5775, 6125, 7392, 8085, 8575, 10976, 11907, 12705, 15625, 16000, 19250, 21120, 21870, 30030, 31104, 32768, 37422, 37730, 40040, 45045, 54675

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

Cf. A000272, A002110, A182318, A260548, A279513, A284763.

Sequence in context: A107737 A045138 A067704 * A192125 A362666 A166270

Adjacent sequences: A284886 A284887 A284888 * A284890 A284891 A284892

Keyword

nonn

Author

Rémy Sigrist, Apr 05 2017

Status

approved