A161994 Composites with an even remainder if divided by the sum of their prime factors.

4, 8, 16, 18, 20, 24, 27, 28, 30, 32, 36, 42, 44, 48, 50, 54, 56, 60, 64, 66, 70, 72, 75, 78, 80, 84, 90, 98, 99, 100, 102, 105, 108, 110, 114, 120, 126, 128, 130, 132, 138, 140, 144, 150, 152, 154, 156, 160, 162, 168, 170, 174, 180, 182, 184, 186, 190, 192, 195, 196, 198

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 24 2009

Keywords

• nonn
• easy

Comments

The composites A002808(k) have prime factor sums A046343(k). The sequence of remainders, A002808(k) mod A046343(k) = 0, 1, 2, 3, 3, 5, 5, 7, 0, ... is scanned for the even terms, occurring at positions k = 1, 3, 9, 10, 11, ..., and the associated A002808(k) are put into the sequence.

Examples

			The first composite is 4=2*2 and 4 mod (2+2) = 0 is even, so 4 is in the sequence.
The second composite is 6=2*3 and 6 mod (2+3) = 1 is odd, so 6 is not a term.
The third composite is 8=2*2*2 and 8 mod (2+2+2) = 2 is even, so 8 is a term.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002808, A046343.

Programs

Mathematica

cerQ[n_]:=!PrimeQ[n]&&EvenQ[Mod[n,Total[Flatten[Table[First[#], {Last[ #]}]&/@FactorInteger[n]]]]]; Select[Range[2,200],cerQ] (* Harvey P. Dale, Jan 19 2014 *)

Extensions

104 removed by R. J. Mathar, Sep 23 2009