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A220219 Products of primorials where all exponents in its prime factorization are one less than a prime. 2

%I

%S 1,2,4,6,12,16,30,36,48,60,64,144,180,192,210,240,420,576,720,900,960,

%T 1024,1260,1296,1680,2310,2880,3072,3600,4096,4620,5040,5184,6300,

%U 6480,6720,9216,12288,13860,14400

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

%C Erdős & Mirsky call these B-numbers.

%H Amiram Eldar, <a href="/A220219/b220219.txt">Table of n, a(n) for n = 1..10000</a>

%H P. Erdős and L. Mirsky, <a href="http://www.renyi.hu/~p_erdos/1952-12.pdf">The distribution of values of the divisor function d(n)</a>, Proc. London Math. Soc. 2 (1952), pp. 257-271.

%F 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....

%o (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)

%Y Intersection of A025487 and A220218.

%K nonn

%O 1,2

%A _Charles R Greathouse IV_, Dec 07 2012

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Last modified August 13 19:30 EDT 2020. Contains 336451 sequences. (Running on oeis4.)