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

1,1

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

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

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

Cf. A002808, A046343.

Sequence in context: A123535 A312765 A065192 * A195065 A312766 A312767

Adjacent sequences: A161991 A161992 A161993 * A161995 A161996 A161997

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Jun 24 2009

Extensions

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

Status

approved