OFFSET
1,60
COMMENTS
A semiprime (A001358) is a product of any two prime numbers. In the even case, these factorizations have A001222(n)/2 factors. - Gus Wiseman, Dec 31 2020
Records 1, 2, 3, 4, 5, 9, 13, 15, 17, ... occur at 1, 60, 210, 840, 1260, 4620, 27720, 30030, 69300, ...
LINKS
FORMULA
EXAMPLE
a(4) = 1, as there is just one way to factor 4 into distinct semiprimes, namely as {4}.
From Gus Wiseman, Dec 31 2020: (Start)
The a(n) factorizations for n = 60, 210, 840, 1260, 4620, 12600, 18480:
4*15 6*35 4*6*35 4*9*35 4*15*77 4*6*15*35 4*6*10*77
6*10 10*21 4*10*21 4*15*21 4*21*55 4*6*21*25 4*6*14*55
14*15 4*14*15 6*10*21 4*33*35 4*9*10*35 4*6*22*35
6*10*14 6*14*15 6*10*77 4*9*14*25 4*10*14*33
9*10*14 6*14*55 4*10*15*21 4*10*21*22
6*22*35 6*10*14*15 4*14*15*22
10*14*33 6*10*14*22
10*21*22
14*15*22
(End)
MATHEMATICA
Table[Count[Subsets[Select[Divisors[n], PrimeOmega[#] == 2 &]], _?(Times @@ # == n &)], {n, 105}] (* Michael De Vlieger, Dec 11 2020 *)
PROG
(PARI) A322353(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((2==bigomega(d)&&(d<=m)), s += A322353(n/d, d-1))); (s)); \\ Antti Karttunen, Dec 10 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 06 2018
STATUS
approved