A284763 -id:A284763 - cp's OEIS frontend

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

Rémy Sigrist, Apr 05 2017

nonn

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.

			1626625 = 5^3*7*11*13^2 appears in this sequence.

Rémy Sigrist, Table of n, a(n) for n = 1..500
Rémy Sigrist, Illustration of the first terms

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

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

cp's OEIS Frontend

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

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