A182277 Quartan semiprimes: semiprimes of the form x^4 + y^4, x>0, y>0.

82, 626, 706, 1921, 2402, 4097, 6497, 6817, 7186, 8962, 10001, 10081, 14642, 17042, 18737, 20737, 21202, 21361, 23137, 24641, 28562, 28642, 29186, 29857, 35377, 38417, 38497, 43202, 44977, 50641, 53026, 53057, 65266, 67937, 72097, 83522, 83602, 84146, 84817, 85922

Offset: 1

Author

Jonathan Vos Post, Apr 22 2012

Keywords

• nonn

Comments

This is to A002645 as A001358 semiprimes is to A000040 primes.

Examples

			a(1) = 3^4 + 1^4 = 82 = 2 * 41.
		

References

• George Greaves, On the representation of a number as a sum of two fourth powers, MATHEMATISCHE ZEITSCHRIFT, Volume 94, Number 3 (1966), 223-234, DOI: 10.1007/BF01111351.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003336 Numbers that are the sum of 2 nonzero 4th powers, A002645 Quartan primes: primes of the form x^4 + y^4, x>0, y>0.

Programs

PARI

issemi(n)=bigomega(n)==2
list(lim)=my(v=List(),t);for(x=1,(lim+.5)^(1/4),for(y=1,min(x,(lim-x^4 + .5)^(1/4)),if(issemi(t=x^4+y^4),listput(v,t))));vecsort(Vec(v),,8) \\ Charles R Greathouse IV, Apr 22 2012

Formula

A001358 INTERSECTION A003336.

Extensions

a(12)-a(40) from Charles R Greathouse IV, Apr 22 2012