A081310 Numbers having no representation as sum of a prime and an 3-smooth number.

1, 2, 36, 78, 96, 120, 126, 144, 156, 162, 186, 204, 210, 216, 222, 276, 288, 300, 306, 324, 328, 330, 336, 342, 366, 372, 378, 396, 408, 414, 426, 438, 456, 474, 486, 498, 516, 528, 534, 540, 546, 552, 562, 576, 582, 606, 612, 624, 630, 636, 666, 672, 690

Offset: 1

Author

Reinhard Zumkeller, Mar 17 2003

Keywords

• nonn

Comments

Complement of A081311.

Examples

			For all primes p<36 the greatest prime factor of 36-p is >3: 36-2=2*17, 36-3=3*11, 36-5=31, 36-7=29, 36-11=5*5, 36-13=23, 36-17=19, 36-19=17, 36-23=13, 36-29=7, 36-31=5, therefore 36 is a term.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A003586, A081308, A081311.

Programs

Haskell

a081310 n = a081310_list !! (n-1)
a081310_list = filter ((== 0) . a081308) [1..]
-- Reinhard Zumkeller, Jul 04 2012

Mathematica

nmax = 1000;
S = Select[Range[nmax], Max[FactorInteger[#][[All, 1]]] <= 3 &];
A081308[n_] := Count[TakeWhile[S, # < n &], s_ /; PrimeQ[n - s]];
Select[Range[nmax], A081308[#] == 0 &] (* Jean-François Alcover, Oct 13 2021 *)

Formula

A081308(a(n)) = 0.