A211176 Numbers n which are the hypotenuse of a Pythagorean triple with n' as a leg, where n' is the arithmetic derivative of n.

125, 625, 23125, 142805, 210125, 371293, 7983625, 9370805, 25757525, 50062025, 120670225, 489766225, 881052625, 1471596725, 2307267625, 2489771125, 3145529225, 3474871553, 6975757441, 7977558641

Offset: 1

Author

Paolo P. Lava, Feb 01 2013

Keywords

• nonn
• more

Comments

This sequence is a subsequence of A008846. - Ray Chandler, Jan 27 2017

Examples

			n = 23125, n' = 19125 and sqrt(n^2-n'^2) = 13000.
		

Crossrefs

Cf. A002144, A002365, A002366, A003415, A008846, A009003, A009004, A210503.

Programs

Maple

with(numtheory); ListA211176:= proc(q)local a,n,p;
for n from 2 to q do a:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);
if n<>a and type(sqrt(n^2-a^2),integer) then print(n); fi;
od; end: ListA211176(10^9);

Formula

A002144(n)^A002365(n) and A002144(n)^A002366(n) are terms of the sequence for all n. - Ray Chandler, Jan 27 2017

Extensions

Name and Maple program corrected by Paolo P. Lava, Sep 30 2013

a(12)-a(16) from Donovan Johnson, Sep 30 2013

a(17)-a(18) from Ray Chandler, Jan 25 2017

a(19)-a(20) from Ray Chandler, Jan 27 2017