A249747 a(n) = floor((A002110(n) * A054272(n)) / A001248(n)).

1, 2, 8, 51, 496, 6041, 97155, 1746481, 38377034, 1053921489, 31722366805, 1127475187757, 45429396874080, 1910408631449923, 87682336584597009, 4571067440374822934, 260160909199262899454, 15823372061924831882182, 1034588557961336117180784, 72606463908572608290939197, 5235472173106695729625747152, 407296805992490241506213234700

Offset: 1

Author

Antti Karttunen, Dec 08 2014

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000010, A001248, A002110, A005867, A054272.

Programs

PARI

default(primelimit, 2^31 + 2^30);
A002110(n) = prod(i=1, n, prime(i));
A054272(n) = 1 + primepi(prime(n)^2) - n;
A249747(n) = (A054272(n)*A002110(n))\(prime(n)^2);
for(n=1, 100, write("b249747.txt", n, " ", A249747(n)));

Formula

a(n) = floor((A002110(n) * A054272(n)) / A001248(n)).

The ratio a(n) / A005867(n) seems to stay near 1. Note that A005867(n) = A000010(A002110(n)). See also formulas in A054272.