A284646 Variation on Leyland numbers: k = x'^y + y'^x, where x' and y' are the arithmetic derivative of x and y.

2, 17, 26, 37, 50, 65, 82, 101, 126, 145, 170, 197, 217, 226, 257, 325, 344, 362, 401, 442, 485, 512, 513, 577, 626, 677, 730, 785, 901, 962, 1001, 1025, 1090, 1157, 1297, 1445, 1522, 1601, 1682, 1729, 1765, 1850, 1937, 2026, 2117, 2198, 2305, 2402, 2501, 2602

Offset: 1

Author

Paolo P. Lava, Mar 31 2017

Keywords

• nonn

Comments

Another similar variation on Leyland numbers is k = x^y' + y^x' that leads to A014091.

Examples

			2' = 1, 4' = 4, 1^4 + 4^2 = 1 + 16 = 17.
		

Crossrefs

Cf. A014091, A076980.

Programs

Maple

with(numtheory): N:= 10^5: A:={}: for x from 2 to floor(N^(1/2)) do
for y from 2 do yd:=y*add(op(2,p)/op(1,p),p=ifactors(y)[2]); xd:=x*add(op(2,p)/op(1,p),p=ifactors(x)[2]); a:= xd^y + yd^x;
if a>N then break fi; A:=A union {a}; od; od; sort([op(A)]);
# based on Robert Israel code in A076980.