OFFSET
1,2
COMMENTS
A semiprime (A001358) is a product of any two prime numbers.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Degree Sequence.
EXAMPLE
The sequence of terms together with their one factorization begins:
1 = 29 = 29 80 = 2*4*10
2 = 2 31 = 31 83 = 83
3 = 3 37 = 37 89 = 89
4 = 4 41 = 41 97 = 97
5 = 5 43 = 43 101 = 101
7 = 7 47 = 47 103 = 103
8 = 2*4 48 = 2*4*6 107 = 107
9 = 9 49 = 49 109 = 109
11 = 11 53 = 53 112 = 2*4*14
13 = 13 59 = 59 113 = 113
17 = 17 61 = 61 121 = 121
19 = 19 67 = 67 125 = 5*25
23 = 23 71 = 71 127 = 127
25 = 25 73 = 73 131 = 131
27 = 3*9 79 = 79 137 = 137
For example, we have 360 = 2*3*6*10, so 360 is in the sequence. But 360 is absent from A293511, because we also have 360 = 2*6*30.
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Select[Range[100], Length[Select[facs[#], UnsameQ@@#&&SubsetQ[{1, 2}, PrimeOmega/@#]&]]==1&]
CROSSREFS
See link for additional cross-references.
These are the positions of ones in A339839.
The version for no factorizations is A339840.
The version for at least one factorization is A339889.
A001055 counts factorizations.
A037143 lists primes and semiprimes.
A293511 are a product of distinct squarefree numbers in exactly one way.
A320663 counts non-isomorphic multiset partitions into singletons or pairs.
A338915 counts partitions that cannot be partitioned into distinct pairs.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 25 2020
STATUS
approved