%I #46 Apr 22 2024 08:38:00

%S 30,42,60,66,70,78,84,90,102,105,110,114,120,126,130,132,138,140,150,

%T 154,156,165,168,170,174,180,182,186,190,195,198,204,210,220,222,228,

%U 230,231,234,238,240,246,252,255,258,260,264,266,270,273,276,280,282,285

%N Numbers that are divisible by at least three different primes.

%C a(n+1)-a(n) seems bounded and sequence appears to give n such that the number of integers of the form nk/(n+k) k>=1 is not equal to Sum_{ d | n} omega(d) (i.e., n such that A062799(n) is not equal to A063647(n)). - _Benoit Cloitre_, Aug 27 2002

%C The first differences are bounded: clearly a(n+1) - a(n) <= 30. - _Charles R Greathouse IV_, Dec 19 2011

%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.

%H Vincenzo Librandi, <a href="/A000977/b000977.txt">Table of n, a(n) for n = 1..10000</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%F a(n) = n + O(n log log n / log n). - _Charles R Greathouse IV_, Dec 19 2011 A001221(a(n)) > 2. - _Reinhard Zumkeller_, May 03 2013

%F A033992 UNION A033993 UNION A051270 UNION A074969 UNION A176655 UNION ... - _R. J. Mathar_, Dec 05 2016

%p A000977 := proc(n)

%p if (nops(numtheory[factorset](n)) >= 3) then

%p RETURN(n)

%p fi: end: seq(A000977(n), n=1..500); # _Jani Melik_, Feb 24 2011

%t DeleteCases[Table[If[Count[PrimeQ[Divisors[i]], True] >= 3, i, 0], {i, 1, 274}], 0]

%t Select[Range[300], PrimeNu[#] >= 3 &] (* _Paolo Xausa_, Mar 28 2024 *)

%o (PARI) is(n)=omega(n)>2 \\ _Charles R Greathouse IV_, Dec 19 2011

%o (Haskell)

%o a000977 n = a000977_list !! (n-1)

%o a000977_list = filter ((> 2) . a001221) [1..]

%o -- _Reinhard Zumkeller_, May 03 2013

%Y Cf. A000961, A007774, A033992, A033993, A051270.

%Y Complement of A070915.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

%E More terms from Vit Planocka (planocka(AT)mistral.cz), Sep 17 2002