%I #18 Apr 04 2023 22:18:22

%S 1,2,3,4,6,10,11,13,14,15,16,20,26,27,29,30,34,36,40,43,48,49,50,56,

%T 58,62,64,76,86,92,94,102,104,106,122,126,130,146,148,176,178,202,211,

%U 218,227,232,238,246,248,262,272,281,286,310,311,326,335,344,346,349,370

%N Numbers whose square cannot be expressed as the sum of a positive square, a positive cube and a positive fourth power.

%C Complement to A180241 with respect to the set of positive integers.

%C If k^2 = m^2 + t^3 + u^4 where k, m, t and u are positive then k^2 - m^2 = (k - m)*(k + m) = t^3 + u^4 which might ease the search for terms by looking at divisors of t^3 + u^4. - _David A. Corneth_, Apr 03 2023

%H David A. Corneth, <a href="/A180242/b180242.txt">Table of n, a(n) for n = 1..3170</a> (terms <= 10^7)

%e a(5) = 6 since 6^2 = 36 cannot be expressed as the sum of a square, a cube and a fourth power.

%o (PARI) for(D=1,99,for(C=1,sqrtn(D^2-1,4),for(B=1,sqrtn(D^2-C^4-1,3),issquare(D^2-C^4-B^3)&&next(3)));print1(D",")) \\ _M. F. Hasler_, Apr 06 2015

%o (PARI) is(n)=my(n2=n^2); for(C=1, sqrtn(n2-1, 4), my(t=n2-C^4); for(B=1, sqrtn(t-1, 3), if(issquare(t-B^3), return(0)))); 1 \\ _Charles R Greathouse IV_, Apr 06 2015

%Y Cf. A180241, A255830, A256091, A256613.

%K nonn

%O 1,2

%A _Carmine Suriano_, Aug 19 2010

%E Name clarified by _David A. Corneth_, Mar 20 2023