

A181818


Products of superprimorials (A006939).


29



1, 2, 4, 8, 12, 16, 24, 32, 48, 64, 96, 128, 144, 192, 256, 288, 360, 384, 512, 576, 720, 768, 1024, 1152, 1440, 1536, 1728, 2048, 2304, 2880, 3072, 3456, 4096, 4320, 4608, 5760, 6144, 6912, 8192, 8640, 9216, 11520, 12288, 13824, 16384, 17280, 18432, 20736, 23040, 24576, 27648, 32768
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Sorted list of positive integers with a factorization Product p(i)^e(i) such that (e(1)  e(2)) >= (e(2)  e(3)) >= ... >= (e(i1)  e(i)) >= e(i).
Subsequence of A025487. A025487(n) belongs to this sequence iff A181815(n) is a member of A025487.
If prime signatures are considered as partitions, these are the members of A025487 whose prime signature is conjugate to the prime signature of a member of A182863.  Matthew Vandermast, May 20 2012


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


FORMULA

Intersection of A055932 and A304686.  Gus Wiseman, Aug 12 2020


EXAMPLE

2, 12, and 360 are all superprimorials (i.e., members of A006939). Therefore, 2*2*12*360 = 17280 is included in the sequence.
From Gus Wiseman, Aug 12 2020 (Start):
The sequence of factorizations (which are unique) begins:
1 = empty product
2 = 2
4 = 2*2
8 = 2*2*2
12 = 12
16 = 2*2*2*2
24 = 2*12
32 = 2*2*2*2*2
48 = 2*2*12
64 = 2*2*2*2*2*2
96 = 2*2*2*12
128 = 2*2*2*2*2*2*2
144 = 12*12
192 = 2*2*2*2*12
256 = 2*2*2*2*2*2*2*2
(End)


MATHEMATICA

Select[Range[100], PrimePi[First/@If[#==1, {}, FactorInteger[#]]]==Range[PrimeNu[#]]&&LessEqual@@Differences[Append[Last/@FactorInteger[#], 0]]&] (* Gus Wiseman, Aug 12 2020 *)


CROSSREFS

A181817 rearranged in numerical order. Also includes all members of A000079, A001021, A006939, A009968, A009992, A066120, A166475, A167448, A181813, A181814, A181816, A182763.
Subsequence of A025487, A087980, A130091, A181824.
A001013 is the version for factorials.
A336426 is the complement.
A336496 is the version for superfactorials.
A001055 counts factorizations.
A006939 lists superprimorials or Chernoff numbers.
A317829 counts factorizations of superprimorials.
Cf. A022915, A055932, A076954, A304686, A325368, A336419, A336420, A336421.
Sequence in context: A116882 A069519 A087980 * A336496 A317804 A328524
Adjacent sequences: A181815 A181816 A181817 * A181819 A181820 A181821


KEYWORD

nonn


AUTHOR

Matthew Vandermast, Nov 30 2010


STATUS

approved



