A274015 Least number of the form x^2 + y^4 in exactly n ways where x and y are nonzero integers.

2, 17, 3026, 141457, 4740625, 113260225, 205117028945, 3234825286225

Offset

1,1

Links

Table of n, a(n) for n=1..8.

Example

a(1) = 2 = 1^2 + 1^4.
a(2) = 17 = 1^2 + 2^4 = 4^2 + 1^4.
a(3) = 3026 = 25^2 + 7^4 = 49^2 + 5^4 = 55^2 + 1^4.
a(4) = 141457 = 191^2 + 18^4 = 321^2 + 14^4 = 336^2 + 13^4 = 376^2 + 3^4.
a(5) = 4740625 = 2177^2 + 6^4 = 2175^2 + 10^4 = 1800^2 + 35^4 = 800^2 + 45^4 = 513^2 + 46^4.
a(6) = 113260225 = 10640^2 + 15^4 = 10593^2 + 32^4 = 10368^2 + 49^4 = 10015^2 + 60^4 = 7967^2 + 84^4 = 5640^2 + 95^4.

Prog

(PARI) do(lim, stride=10^7)=lim\=1; my(v, t, r, top); forstep(n=0, lim-1, stride, top=min(n+stride, lim); v=vectorsmall(top-n); for(y=1, sqrtnint(top-1, 4), t=y^4; for(x=if(n>t, sqrtint(n-t)+1, 1), sqrtint(top-t), v[t+x^2-n]++)); for(i=1, #v, if(v[i]>r, r=v[i]; print(r" "i+n)))) \\ Charles R Greathouse IV, Jun 07 2016

Crossrefs

Cf. A111925.

Sequence in context: A092415 A274053 A221207 * A279884 A060353 A002814

Adjacent sequences: A274012 A274013 A274014 * A274016 A274017 A274018

Keyword

nonn,more

Author

Altug Alkan, Jun 06 2016

Extensions

a(5)-a(6) from Charles R Greathouse IV, Jun 07 2016

a(7)-a(8) from Giovanni Resta, Jun 07 2016

Status

approved