OFFSET
1,1
COMMENTS
A semiprime (A001358) is a product of any two not necessarily distinct primes.
If A025487(k) is in the sequence then so is every number with the same prime signature. - David A. Corneth, Oct 23 2018
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
EXAMPLE
A complete list of all factorizations of 1296 into semiprimes is:
1296 = (4*4*9*9)
1296 = (4*6*6*9)
1296 = (6*6*6*6)
None of these is strict, so 1296 belongs to the sequence.
MATHEMATICA
strsemfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[strsemfacs[n/d], Min@@#>d&]], {d, Select[Rest[Divisors[n]], PrimeOmega[#]==2&]}]];
Select[Range[1000], And[EvenQ[PrimeOmega[#]], strsemfacs[#]=={}]&]
PROG
(PARI)
A322353(n, m=n, facs=List([])) = if(1==n, my(u=apply(bigomega, Vec(facs))); (0==length(u)||(2==vecmin(u)&&2==vecmax(u))), my(s=0, newfacs); fordiv(n, d, if((d>1)&&(d<=m), newfacs = List(facs); listput(newfacs, d); s += A322353(n/d, d-1, newfacs))); (s));
isA300892(n) = if(bigomega(n)%2, 0, (0==A322353(n))); \\ Antti Karttunen, Dec 06 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2018
STATUS
approved