A086046 Sum of first n 4-almost primes.

16, 40, 76, 116, 170, 226, 286, 367, 451, 539, 629, 729, 833, 959, 1091, 1226, 1362, 1502, 1652, 1804, 1960, 2144, 2333, 2529, 2727, 2931, 3141, 3361, 3586, 3814, 4046, 4280, 4528, 4778, 5038, 5314, 5608, 5904, 6201, 6507, 6815, 7130, 7458, 7788, 8128

Offset: 1

Author

Shyam Sunder Gupta, Aug 24 2003

Keywords

• easy
• nonn

Comments

Elements in this sequence can themselves be 4-almost primes. a(1) = 16 = 2^4. a(2) = 40 = 2^3 * 5. a(19) = 1652 = 2^2 * 7 * 59. a(20) = 1804 = 2^2 * 11 * 41. a(31) = 4046 = 2 * 7 * 17^2. a(37) = 5608 = 2^3 * 701. a(39) = 6201 = 3^2 * 13 * 53. a(40) = 6507 = 3^3 * 241. a(42) = 7130 = 2 * 5 * 23 * 31. a(43) = 7458 = 2 * 3 * 11 * 113. Does this happen infinitely often? - Jonathan Vos Post, Dec 11 2004

Examples

			a(2)=40 because sum of first two 4-almost primes i.e. 16+24 is 40.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Mathematica

Accumulate[Select[Range[1000],PrimeOmega[#]==4&]] (* Harvey P. Dale, Feb 07 2014 *)

Formula

a(n) = sum_{i=1..n} A014613(i). - R. J. Mathar, Sep 14 2012