A076771 Even numbers n representable as the sum of two non-coprime odd composites.

18, 24, 30, 36, 40, 42, 48, 50, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 98, 100, 102, 104, 108, 110, 112, 114, 120, 126, 130, 132, 136, 138, 140, 144, 150, 152, 154, 156, 160, 162, 168, 170, 174, 176, 180, 182, 184, 186, 190, 192, 196, 198, 200, 204

Offset

1,1

Comments

It is conjectured that there is no N such that for all n > N, every even number is represented.

The conjecture is true since 2p, p prime, is never a member of this sequence. - Charles R Greathouse IV, Aug 08 2011

An equivalent definition of this sequence: even numbers n such that phi(n) < (n-4)/2. - Arkadiusz Wesolowski, Aug 08 2011

Also: products of an even number >= 6 and an odd number >= 3. - Charles R Greathouse IV, Aug 08 2011

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000

Example

40 = 5*(3 + 5).

Prog

(PARI) upTo(lim)=my(v=List()); forstep(a=6, lim\3, 2, forstep(b=3, lim\a, 2, listput(v, a*b))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Aug 08 2011
(PARI) upTo(lim)=my(v=List(), p=7, m); forprime(q=8, lim\2, forstep(n=p+2, q-2, 2, m=n; while((m<<=1)<=lim, listput(v, m))); p=q); forstep(n=2*p+4, lim, 4, listput(v, n)); forprime(p=3, lim>>3, m=p<<3; while(m<=lim, listput(v, m); m<<=1)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Aug 08 2011

Crossrefs

Cf. A161962.

Sequence in context: A076770 A105679 A160810 * A375162 A179014 A105093

Adjacent sequences: A076768 A076769 A076770 * A076772 A076773 A076774

Keyword

nonn,easy

Author

Jon Perry, Nov 14 2002

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 08 2011

Status

approved