1,1

This is to 5-almost primes as A122093 is to 4-almost primes as A122032 is to 3-almost primes and as A122019 is to 2-almost primes (semiprimes). Note that these can nonmonotonic (look at the graphs). What is the asymptotic value of the ratio A014614(n)/A002110(n)?

a(n) = floor(A122123(n)/A002110(n)) = floor(Prod(i=1..n)5almostprime(i)/Prod(i=1..n)prime(i)) = floor(Prod(i=1..n)A014614(i)/Prod(i=1..n)A000040(i)) = floor(Prod(i=1..n)(A014614(i)/A000040(i))).

a(1) = floor(32/2) = floor 16 = 16.

a(2) = floor(1536/6) = floor(256) = 256.

a(3) = floor(110592/30) = floor(3686.4) = 3686.

a(4) = floor(8847360/210) = floor(42130.2857) = 42130.

a(5) = floor(955514880/2310) = floor(413642.805) = 413642.

a(6) = floor(107017666560/30030) = floor(3563691.86) = 3563691.

a(7) = floor(12842119987200/510510) floor(61152952320/2431) = floor(25155471.95) = 25155471.

a(8) = floor(2080423437926400/9699690) = floor(214483497.712) = 214483497.

a(9) = floor(349511137571635200/223092870) = floor(1566662070.247) = 1566662070.

a(10) = floor(61513960212607795200/6469693230) = floor(9508018081.501) = 9508018081.

Cf. A001222, A002110, A008585, A014613, A008587, A086046, A086047, A122093, A112141, A114426, A014614.

Adjacent sequences: A122606 A122607 A122608 this_sequence A122610 A122611 A122612

Sequence in context: A135554 A017570 A016744 this_sequence A136577 A001025 A067223

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Oct 20 2006