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A284889 Numbers n such that A279513(n) is a primorial number (A002110). 1
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 (list; graph; refs; listen; history; text; internal format)
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 A166270 A129459

Adjacent sequences:  A284886 A284887 A284888 * A284890 A284891 A284892

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Apr 05 2017

STATUS

approved

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Last modified May 7 19:41 EDT 2021. Contains 343652 sequences. (Running on oeis4.)