A220264 Smallest integer with exactly n semiprime divisors.

1, 4, 12, 30, 60, 180, 210, 420, 1260, 6300, 2310, 4620, 13860, 69300, 485100, 30030, 60060, 180180, 900900, 6306300, 69369300, 510510, 1021020, 3063060, 15315300, 107207100, 1179278100, 15330615300, 9699690, 19399380, 58198140, 290990700, 2036934900, 22406283900

Offset

0,2

Comments

At the Mar 31 2011 suggestion of Zak Seidov in A086971.

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

All terms are cubefree products of primorials (A025487 INTERSECT A004709). - Charles R Greathouse IV, Dec 11 2012

A086971(a(n)) = n and A086971(m) != n for m < a(n). - Reinhard Zumkeller, Dec 14 2012

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Mathematica

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

Prog

(PARI) prim(n)=my(v=primes(n)); prod(i=1, #v, v[i])
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
(Haskell)
import Data.List (find); import Data.Maybe (fromJust)
a220264 n = fromJust $ find ((== n) . a086971) a220423_list
-- Reinhard Zumkeller, Sep 08 2015

Crossrefs

Subsequence of A220423.

Sequence in context: A047177 A048077 A350424 * A367097 A212519 A166213

Adjacent sequences: A220261 A220262 A220263 * A220265 A220266 A220267

Keyword

nonn,easy

Author

Robert G. Wilson v, Dec 09 2012

Extensions

a(25)-a(26) from Donovan Johnson, Dec 10 2012

a(27)-a(41) from Charles R Greathouse IV, Dec 11 2012

Status

approved