login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A320892 Numbers with an even number of prime factors (counted with multiplicity) that cannot be factored into distinct semiprimes. 36
16, 64, 81, 96, 144, 160, 224, 256, 324, 352, 384, 400, 416, 486, 544, 576, 608, 625, 640, 729, 736, 784, 864, 896, 928, 960, 992, 1024, 1184, 1215, 1296, 1312, 1344, 1376, 1408, 1440, 1504, 1536, 1600, 1664, 1696, 1701, 1888, 1936, 1944, 1952, 2016, 2025 (list; graph; refs; listen; history; text; internal format)
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
Numbers for which A001222(n) is even and A322353(n) is zero. - Antti Karttunen, Dec 06 2018
LINKS
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
Sequence in context: A303797 A118902 A092210 * A365263 A062320 A233330
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 10:53 EDT 2024. Contains 371240 sequences. (Running on oeis4.)