

A161994


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


1



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
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OFFSET

1,1


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.


LINKS



EXAMPLE

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.


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 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



