login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

a(n) = the smallest integer > n that is divisible by exactly the same number of distinct primes as n is.
5

%I #13 Mar 11 2014 01:32:48

%S 3,4,5,7,10,8,9,11,12,13,14,16,15,18,17,19,20,23,21,22,24,25,26,27,28,

%T 29,33,31,42,32,37,34,35,36,38,41,39,40,44,43,60,47,45,46,48,49,50,53,

%U 51,52,54,59,55,56,57,58,62,61,66,64,63,65,67,68,70,71,69,72,78,73,74

%N a(n) = the smallest integer > n that is divisible by exactly the same number of distinct primes as n is.

%H Reinhard Zumkeller, <a href="/A165713/b165713.txt">Table of n, a(n) for n = 2..10000</a>

%e 12 = 2^2 *3, and so is divisible by exactly 2 distinct primes. The next larger number divisible by exactly 2 distinct primes is 14, which is 2*7. So a(12) = 14.

%t a[n_] := For[nu = PrimeNu[n]; k = n+1, True, k++, If[PrimeNu[k] == nu, Return[k]]]; Table[a[n], {n, 2, 100}] (* _Jean-François Alcover_, Nov 18 2013 *)

%o (Haskell)

%o a165713 n = head [x | x <- [n + 1 ..], a001221 x == a001221 n]

%o -- _Reinhard Zumkeller_, Aug 29 2013

%Y Cf. A165712, A137929.

%Y Cf. A001221, A079892.

%K nonn

%O 2,1

%A _Leroy Quet_, Sep 24 2009

%E More terms from _Sean A. Irvine_, Feb 10 2010