A220264 - OEIS

%I #33 Aug 17 2023 08:16:36

%S 1,4,12,30,60,180,210,420,1260,6300,2310,4620,13860,69300,485100,

%T 30030,60060,180180,900900,6306300,69369300,510510,1021020,3063060,

%U 15315300,107207100,1179278100,15330615300,9699690,19399380,58198140,290990700,2036934900,22406283900

%N Smallest integer with exactly n semiprime divisors.

%C At the Mar 31 2011 suggestion of _Zak Seidov_ in A086971.

%C Often a(n+1) = k*a(n) for some integer k.

%C All terms are cubefree products of primorials (A025487 INTERSECT A004709). - _Charles R Greathouse IV_, Dec 11 2012

%C A086971(a(n)) = n and A086971(m) != n for m < a(n). - _Reinhard Zumkeller_, Dec 14 2012

%H Charles R Greathouse IV, <a href="/A220264/b220264.txt">Table of n, a(n) for n = 0..10000</a>

%t semiPrimeQ[n_] := PrimeOmega@ n == 2; f[n_] := Length@ Select[Divisors@ n, semiPrimeQ@# &]; t = Table[0, {50}]; k = 1; While[k < 10^7, a = f@ k; If[t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++]; t

%o (PARI) prim(n)=my(v=primes(n));prod(i=1,#v,v[i])

%o a(n)=if(n>1,my(L=(sqrtint(8*n+1)+1)\2);prim(L)*prim(n-binomial(L,2)),1+3*n) \\ _Charles R Greathouse IV_, Dec 11 2012

%o (Haskell)

%o import Data.List (find); import Data.Maybe (fromJust)

%o a220264 n = fromJust $ find ((== n) . a086971) a220423_list

%o -- _Reinhard Zumkeller_, Sep 08 2015

%Y Subsequence of A220423.

%K nonn,easy

%O 0,2

%A _Robert G. Wilson v_, Dec 09 2012

%E a(25)-a(26) from _Donovan Johnson_, Dec 10 2012

%E a(27)-a(41) from _Charles R Greathouse IV_, Dec 11 2012