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

Author

Robert G. Wilson v, Dec 09 2012

Keywords

• nonn
• easy

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

Crossrefs

Subsequence of A220423.

Programs

Haskell

import Data.List (find); import Data.Maybe (fromJust)
a220264 n = fromJust $ find ((== n) . a086971) a220423_list
-- Reinhard Zumkeller, Sep 08 2015

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

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

Extensions

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

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