cp's OEIS Frontend

A339191 Partial products of squarefree semiprimes (A006881).

%I A339191 #11 Dec 02 2020 18:48:05
%S A339191 6,60,840,12600,264600,5821200,151351200,4994589600,169816046400,
%T A339191 5943561624000,225855341712000,8808358326768000,405184483031328000,
%U A339191 20664408634597728000,1136542474902875040000,64782921069463877280000,3757409422028904882240000
%N A339191 Partial products of squarefree semiprimes (A006881).
%C A339191 A squarefree semiprime is a product of any two distinct prime numbers.
%C A339191 Do all terms belong to A242031 (weakly decreasing prime signature)?
%e A339191 The sequence of terms together with their prime indices begins:
%e A339191           6: {1,2}
%e A339191          60: {1,1,2,3}
%e A339191         840: {1,1,1,2,3,4}
%e A339191       12600: {1,1,1,2,2,3,3,4}
%e A339191      264600: {1,1,1,2,2,2,3,3,4,4}
%e A339191     5821200: {1,1,1,1,2,2,2,3,3,4,4,5}
%e A339191   151351200: {1,1,1,1,1,2,2,2,3,3,4,4,5,6}
%e A339191 The sequence of terms together with their prime signatures begins:
%e A339191                    6: (1,1)
%e A339191                   60: (2,1,1)
%e A339191                  840: (3,1,1,1)
%e A339191                12600: (3,2,2,1)
%e A339191               264600: (3,3,2,2)
%e A339191              5821200: (4,3,2,2,1)
%e A339191            151351200: (5,3,2,2,1,1)
%e A339191           4994589600: (5,4,2,2,2,1)
%e A339191         169816046400: (6,4,2,2,2,1,1)
%e A339191        5943561624000: (6,4,3,3,2,1,1)
%e A339191      225855341712000: (7,4,3,3,2,1,1,1)
%e A339191     8808358326768000: (7,5,3,3,2,2,1,1)
%e A339191   405184483031328000: (8,5,3,3,2,2,1,1,1)
%t A339191 FoldList[Times,Select[Range[20],SquareFreeQ[#]&&PrimeOmega[#]==2&]]
%Y A339191 A000040 lists the primes, with partial products A002110 (primorials).
%Y A339191 A001358 lists semiprimes, with partial products A112141.
%Y A339191 A002100 counts partitions into squarefree semiprimes (restricted: A338903)
%Y A339191 A000142 lists factorial numbers, with partial products A000178.
%Y A339191 A005117 lists squarefree numbers, with partial products A111059.
%Y A339191 A006881 lists squarefree semiprimes, with partial sums A168472.
%Y A339191 A166237 gives first differences of squarefree semiprimes.
%Y A339191 A320655 counts factorizations into semiprimes.
%Y A339191 A320656 counts factorizations into squarefree semiprimes.
%Y A339191 A338898/A338912/A338913 give prime indices of semiprimes.
%Y A339191 A338899/A270650/A270652 give prime indices of squarefree semiprimes.
%Y A339191 A338901 gives first appearances in the list of squarefree semiprimes.
%Y A339191 A339113 gives products of primes of squarefree semiprime index.
%Y A339191 Cf. A001221, A112798, A167171, A320732, A320891, A320892, A320894, A320911, A338900, A338902, A339003, A339004.
%K A339191 nonn
%O A339191 1,1
%A A339191 _Gus Wiseman_, Nov 30 2020