A000977 Numbers that are divisible by at least three different primes.

30, 42, 60, 66, 70, 78, 84, 90, 102, 105, 110, 114, 120, 126, 130, 132, 138, 140, 150, 154, 156, 165, 168, 170, 174, 180, 182, 186, 190, 195, 198, 204, 210, 220, 222, 228, 230, 231, 234, 238, 240, 246, 252, 255, 258, 260, 264, 266, 270, 273, 276, 280, 282, 285

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

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

References

• 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.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

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

Complement of A070915.

Programs

Haskell

a000977 n = a000977_list !! (n-1)
a000977_list = filter ((> 2) . a001221) [1..]
-- Reinhard Zumkeller, May 03 2013

Maple

A000977 := proc(n)
if (nops(numtheory[factorset](n)) >= 3) then
   RETURN(n)
fi: end:  seq(A000977(n), n=1..500); # Jani Melik, Feb 24 2011

Mathematica

DeleteCases[Table[If[Count[PrimeQ[Divisors[i]], True] >= 3, i, 0], {i, 1, 274}], 0]
Select[Range[300], PrimeNu[#] >= 3 &] (* Paolo Xausa, Mar 28 2024 *)

PARI

is(n)=omega(n)>2 \\ Charles R Greathouse IV, Dec 19 2011

Formula

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

A033992 UNION A033993 UNION A051270 UNION A074969 UNION A176655 UNION ... - R. J. Mathar, Dec 05 2016

Extensions

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