|
%I #13 Jan 27 2014 11:45:46
%S 1,2,3,4,5,6,7,8,9,30,11,12,13,210,15,16,17,18,19,60,105,2310,23,24,
%T 25,30030,27,420,29,30,31,32,1155,510510,35,36,37,9699690,15015,120,
%U 41,210,43,4620,45,223092870,47,48,49,150,255255,60060,53,54,385
%N Least multiple of n having no prime gaps.
%C a(n) = smallest m such that m is a multiple of n and in the prime factorization of m every prime between the smallest prime factor of n and the largest appears at least once.
%C A073490(a(n))=0; a(n)=n iff A073490(A007947(n))=0; A006530(a(n)) = A006530(n); A020639(a(n)) = A020639(n); A001221(n) <= A001221(a(n)); A001221(a(n))=A049084(A006530(n))-A049084(A020639(n))+1; A001222(n) <= A001222(a(n)); A001222(a(n)) + A001221(n) = A001221(a(n)) + A001222(n).
%H Reinhard Zumkeller, <a href="/A072941/b072941.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n)=A002110(A049084(A006530(n)))*A003557(n)/A002110(A049084(A020639(n))-1).
%e a(99)=a(3*3*11)=3*3*5*7*11=3465.
%o (Haskell)
%o a072941 n = product $ zipWith (^) ps $ map (max 1) es where
%o (ps, es) = unzip $ dropWhile ((== 0) . snd) $
%o zip a000040_list $ a067255_row n
%o -- _Reinhard Zumkeller_, Dec 21 2013
%Y Cf. A073490, A074044, A067255.
%K nonn,look
%O 1,2
%A _Reinhard Zumkeller_, Aug 12 2002
%E Example corrected by _Nadia Heninger_, Jul 06 2005
|
