cp's OEIS Frontend

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

%I A284889 #11 Apr 09 2017 10:02:33
%S A284889 1,2,6,8,9,30,40,45,75,96,210,250,280,315,486,525,672,735,1750,1920,
%T A284889 2310,3080,3402,3430,3465,5775,6125,7392,8085,8575,10976,11907,12705,
%U A284889 15625,16000,19250,21120,21870,30030,31104,32768,37422,37730,40040,45045,54675
%N A284889 Numbers n such that A279513(n) is a primorial number (A002110).
%C A284889 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).
%C A284889 This sequence contains the primorial numbers (A002110); 8 = 2^3 is the first term in this sequence that is not a primorial number.
%C A284889 This sequence contains A260548.
%C A284889 All terms belong to A284763.
%C A284889 If a(n) <= p# for some prime p, then a(n) is p-smooth (p# denotes the product of the primes <= p, see A002110).
%C A284889 There are A000272(k+1) terms with k prime numbers in their prime tower factorization:
%C A284889 - for k=0: 1,
%C A284889 - for k=1: 2,
%C A284889 - for k=2: 2*3, 2^3, 3^2,
%C A284889 - 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.
%H A284889 Rémy Sigrist, <a href="/A284889/b284889.txt">Table of n, a(n) for n = 1..500</a>
%H A284889 Rémy Sigrist, <a href="/A284889/a284889.pdf">Illustration of the first terms</a>
%e A284889 1626625 = 5^3*7*11*13^2 appears in this sequence.
%o A284889 (PARI) isprimorial(n) = if (n==1, 1, my (f=factor(n)); (#f~ == primepi(vecmax(f[,1]))) && (vecmax(f[,2]) == 1));
%o A284889 a279513(n) =  my (f=factor(n)); prod(i=1, #f~, f[i, 1]*a279513(f[i, 2]));
%o A284889 isok(n) = isprimorial(a279513(n)); \\ _Michel Marcus_, Apr 08 2017
%Y A284889 Cf. A000272, A002110, A182318, A260548, A279513, A284763.
%K A284889 nonn
%O A284889 1,2
%A A284889 _Rémy Sigrist_, Apr 05 2017