A220219 Products of primorials where all exponents in its prime factorization are one less than a prime.

1, 2, 4, 6, 12, 16, 30, 36, 48, 60, 64, 144, 180, 192, 210, 240, 420, 576, 720, 900, 960, 1024, 1260, 1296, 1680, 2310, 2880, 3072, 3600, 4096, 4620, 5040, 5184, 6300, 6480, 6720, 9216, 12288, 13860, 14400

Offset: 1

Author

Charles R Greathouse IV, Dec 07 2012

Keywords

• nonn

Comments

Erdős & Mirsky call these B-numbers.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• P. Erdős and L. Mirsky, The distribution of values of the divisor function d(n), Proc. London Math. Soc. 2 (1952), pp. 257-271.

Crossrefs

Intersection of A025487 and A220218.

Programs

PARI

is(n)=my(e=valuation(n,2),e1); if(!isprime(e+1), return(n==1)); n>>=e; forprime(p=3,, if(n==1, return(1)); e1=valuation(n,p); if(!isprime(e1+1) || e1 > e, return(0)); n/=p^e1; e = e1)

Formula

Erdős & Mirsky show that there are exp((k + o(1)) sqrt(log x)/log log x) members of this sequence below x, where k = Pi * sqrt(8/3) = 5.130....