A274027 Numbers k such that k^4 is the average of a positive cube and a positive fifth power.

1, 162, 324, 3888, 11664, 18750, 31250, 32768, 38416, 40000, 160000, 167042, 168750, 253125, 373248, 607500, 911250, 1037232

Offset: 1

Author

Altug Alkan, Jun 07 2016

Keywords

• nonn
• more

Comments

Numbers n such that 2*n^4 is of the form x^3 + y^5 where x and y are positive integers.

Sequence is infinite because if m is a term, that is m^4 = (w^3 + z^5)/2 with w and z positive integers, then m*t^15 is also a term for every integer t>1. In fact: (m*t^15)^4 = ((w*t^20)^3 + (z*t^12)^5)/2.

Examples

			162 = 3*54 is a term because (3*54)^4 = ((18*54)^3 + 54^5)/2.
38416 = 14^4 is a term because (14^4)^4 = ((3*14^5)^3 + (14^3)^5)/2.
		

Crossrefs

Cf. A000583, A100293.

Programs

PARI

isA100293(n) = for(y=1, sqrtnint(n-1, 5), if(ispower(n-y^5, 3), return(1))); 0;
lista(nn) = for(n=1, nn, if(isA100293(2*n^4), print1(n, ", ")));

Extensions

a(11)-a(18) from Giovanni Resta, Jun 07 2016