OFFSET
1,2
COMMENTS
Complement to A180241 with respect to the set of positive integers.
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
LINKS
David A. Corneth, Table of n, a(n) for n = 1..3170 (terms <= 10^7)
EXAMPLE
a(5) = 6 since 6^2 = 36 cannot be expressed as the sum of a square, a cube and a fourth power.
PROG
(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
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Carmine Suriano, Aug 19 2010
EXTENSIONS
Name clarified by David A. Corneth, Mar 20 2023
STATUS
approved