A014134 Numbers that are not the sum of a square (A000290) and a triangular number (A000217).

8, 13, 18, 20, 23, 27, 33, 34, 38, 41, 43, 47, 48, 58, 60, 62, 63, 68, 69, 73, 76, 83, 86, 88, 89, 90, 93, 97, 98, 99, 108, 111, 112, 113, 118, 123, 125, 132, 133, 134, 135, 138, 139, 143, 146, 148, 151, 158, 160, 163, 164, 167, 168, 173, 174

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

n is in the sequence if for some prime p == 5 or 7 (mod 8), 8*n+1 is divisible by p but not by p^2. The first member of the sequence that does not have this property is 16078. - Robert Israel, Mar 17 2015

Links

• R. J. Mathar, Table of n, a(n) for n = 1..4646

Crossrefs

Cf. A140867.

Programs

Maple

N:= 1000: # to generate all terms <= N
{$1 .. N} minus {seq(seq(x*(x+1)/2 + y^2, y = 0 .. floor(sqrt(N - x*(x+1)/2))),
x = 0 .. floor((sqrt(8*N+1)-1)/2))};
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(%,list)); # Robert Israel, Mar 17 2015

Mathematica

fQ[n_] := Block[{k = 0, lmt = 1 + Floor@ Sqrt@ n}, While[k < lmt && !IntegerQ@ Sqrt[ 8(n - k^2) + 1], k++]; k == lmt]; Select[ Range@ 175, fQ@# &] (* Robert G. Wilson v, Nov 29 2015 *)

PARI

is_A014134(n)=for(k=0,sqrtint(n*2),issquare(n-k*(k+1)/2)&return);1 /* M. F. Hasler, Jan 05 2009 */